High Resolution Experimental Studies and Numerical Analysis of Fine Bubble
Ozone Disinfection Contactors
A Thesis
Submitted to the Faculty
of
Drexel University
by
Timothy A. Bartrand
in partial fulfillment of the
requirements for the degree
of
Doctor of Philosophy
Nove
ii
Dedications
This dissertation is dedicated to my wife, Carolyn Davis, and my daughter, Olivia
Bartrand. Few people in my station in life have the opportunity to devote time and effort
to a dissertation. That is because they don’t have a wife and daughter like mine. Thank
you both for the support, the fun, the trips to the lab and office, the loan of parts of the
house to act as my office and, above all, the love you’ve given during this process. May I
do the same for you both.
iii
Ackowledgements
During my dissertation studies, my work was funded by the L.D. Betz
Endowment for Environmental Engineering, the Koerner Family Fellowship, the
Philadelphia Water Department, the Steven Geigerich Schoarship, and the Northeast
Chemical Association. I am deeply grateful for the support of these organizations.
I received technical support from many during the execution of my work.
Without the help of the individuals I mention below, this work would surely have
faltered. My greatest thanks are due to my advisors, Professor Charles Haas and
Professor Bakhtier Farouk. Their assistance to me went beyond technical assistance.
They showed me, through example and in discussions, what research should and could
be. They also shared their knowledge of proposal writing and project development with
me. If, in the future, I should succeed at these endeavors it will be by following their
examples. I am grateful for the oversight and improvements in my dissertation provided
by my other committee members, Prof. Raj Mutharasan, Prof. Wen Shieh and Dr. Jin
Wen.
Others who helped me in my research at Drexel are Blaise Tobia (College of
Media, Arts and Design), who helped develop the lighting scheme I used in experiments,
Gary Burlingame, Philadelphia Water Department, who always opened his door to me
when I called, Nicole Charlton, Philadelphia Water Department, who provided a tour and
data of the Philadelphia Water Department’s pilot reactors, Dr. Patrick Gurian, for
assistance with statistics, Dr. Guibo Xie, for assistance with chemistry, and, last but not
iv
least, Professor Joseph Martin, for helping me find a perfect bubble column
reactor and for good conversations about engineering and beyond.
Kim DiGiovanni, Russell Goodman, Dr. Domenico Santoro, Joanna Pope, Mark
Weir, Arun Kumar and Shamia Hoque all helped in experimental data acquisition.
Thanks to them for their efforts and the cheerful way in which they offered them.
The Civil, Architectural and Environmental staff, Barbara Interlandi, Sharon
Stokes, Ken Holmes and Amanda Gonzales, are to be commended for their willingness to
help students and the collegial way they worked with them.
Finally, I acknowledge the help and camaraderie of my fellow graduate students
not yet mentioned, Dr. Dennis Greene, Dr. Bariş Kaymak, Dr. Lijie Li, Jason Marie, Dr.
Rob Ryan and Jade Blackwell. These students and those mentioned above made my
graduate studies richer and more enjoyable than I could have expected.
v
Table of Contents
LIST OF TABLES..........................................................................................................VIII
LIST OF FIGURES .......................................................................................................... IX
ABSTRACT .............................................................................................................XII
I INTRODUCTION..................................................................................................... 1
I.1 Objectives and Study Overview.................................................................... 7
I.1.1 Objectives ............................................................................................ 8
I.1.2 Overview9
I.2 When and Why Ozone is Used in Water Treatment ................................... 10
I.2.1 Ozone Use in Potable Water Disinfection ......................................... 10
I.2.2 Advantages and Disadvantages of Ozone as a Disinfectant .............. 11
I.3 Ozone Contactor Design ............................................................................. 12
I.3.1 Typical Reactor Designs and Design Parameters .............................. 12
I.3.2 Reactor Design and Scale-up............................................................. 14
I.3.3 Ct Credit16
I.3.4 Roles for CFD within the Regulatory Framework ............................ 25
I.4 CFD in Water and Wastewater Treatment Operations Analysis................. 26
I.5 Need for the Current Study ......................................................................... 28
I.6 Significance of the Proposed Work............................................................. 30
I.6.1 Advancement of Knowledge ............................................................. 30
I.6.2 Value to Industry ............................................................................... 32
II LITERATURE SURVEY ....................................................................................... 35
II.1 Bubble Column Reactor Phenomena .......................................................... 37
II.1.1 Countercurrent Two-phase Flow Modeling....................................... 38
II.1.2 Ozone Demand, Decomposition and Properties................................ 83
II.1.3 Disinfection Byproduct Formation .................................................... 85
II.1.4 Microbial inactivation........................................................................ 90
II.2 Experimental Investigations of Bubble Column Reactors .......................... 94
vi
II.2.1 Experimental Measurement of Mass Transfer in Bubble
Columns ........................................................................................... 95
II.2.2 High-Resolution Study of Bubble Column Hydrodynamics ............. 97
II.3 Ozone Contactor Modeling ......................................................................... 99
II.3.1 CFD Models....................................................................................... 99
II.3.2 Other Models ................................................................................... 109
II.4 Other Bubble Contactor CFD Studies ....................................................... 111
III EXPERIMENTAL METHODS............................................................................ 119
III.1 Experimental Apparatus ............................................................................ 120
III.2 Residence Time Distribution Studies........................................................ 125
III.3 Ozone Mass Transfer Visualization Studies ............................................. 130
III.3.1 Overview ......................................................................................... 130
III.3.2 Indigo Dye Solution Composition and Preparation......................... 132
III.3.3 Photography Methodology .............................................................. 135
III.3.4 Development of Indigo Dye Color Calibration Curve .................... 136
IV NUMERICAL METHODS................................................................................... 143
IV.1 Mathematical Model ................................................................................. 143
IV.2 Numerical Model....................................................................................... 148
IV.3 Model Validation....................................................................................... 151
V COUNTERCURRENT FLOW HYDRODYNAMICS INVESTIGATIONS ...... 154
V.1 Bubble Plume Behavior and Flow Visualization ...................................... 155
V.2 Residence Time Distribution Analysis...................................................... 158
V.3 Numerical Studies ..................................................................................... 164
V.4 Influences of Inlet and Discharge Configurations..................................... 171
V.4.1 Philadelphia Water Department Pilot Disinfection Unit ................. 173
VI MASS TRANSFER STUDIES ............................................................................. 178
VI.1 Matrix of Mass Transfer Studies ............................................................... 178
VI.2 Ozone Mass Transfer Visualization Results ............................................. 180
VI.2.1 Observations .................................................................................... 180
vii
VI.2.2 Parameter Estimates......................................................................... 185
VI.3 CFD Mass Transfer Modeling Results...................................................... 209
VII CRYPTOSPORIDIUM INACTIVATION AND BROMATE FORMATION IN A
FULL-SCALE REACTOR ................................................................................... 224
VII.1 Description of Full Scale Reactor ............................................................. 224
VII.2 Full Scale Reactor CFD Model ................................................................. 226
VII.2.1CFD Model General Features .......................................................... 226
VII.2.2Cryptosporidium Inactivation and Bromate Formation Submodels 228
VII.3 Phase Distribution and Flow Field ............................................................ 229
VII.4 Inactivation and Comparison to Log Credits from Ct Models.................. 237
VIII CONCLUSIONS AND DISCUSSIONS .............................................................. 243
VIII.1 Summary of Major Findings ..................................................................... 243
VIII.2 Details of Major Findings ......................................................................... 243
VIII.3 Using CFD in Design and Scale-up of Ozone Bubble Contactors............ 249
VIII.4 Critical Review of Ozone Mass Transfer Visualization Technique.......... 252
VIII.5 Balancing Acute and Chronic Risks.......................................................... 255
LIST OF REFERENCES................................................................................................ 257
APPENDIX A:LIST OF SYMBOLS ............................................................................. 271
APPENDIX B:LIST OF ABBREVIATIONS AND ACRONYMS............................... 273
APPENDIX C:ANALYSIS OF RADIALLY-AVERAGED IMAGE DATA ............... 274
APPENDIX D:R SCRIPT FOR BEST FIT PARAMETERS ESTIMATION ............... 290
viii
LIST OF TABLES
Table 1: Ct Values for Cryptosporidium Inactivation by Ozone (40 CFR 141.730)......... 5
Table 2: Summary of Disinfection Impacts (United States Environmental ProtectionAgency 1999) ...................................................................................................... 6
Table 3: Advantages and Disadvantages of Ozone as a Disinfectant .............................. 12
Table 4: Guidelines for Selection of Ct Calculation Method .......................................... 17
Table 5: Summary of Bubble Diameter Relations........................................................... 47
Table 6: Summary of Gas Phase Holdup Relations......................................................... 49
Table 7: Dimensionless Parameters Associated with Bubble Drag and Terminal RiseSpeed ................................................................................................................. 51
Table 8: Summary of Bubble Drag Relations.................................................................. 54
Table 9: Summary of Bubble Terminal Speed Relations ................................................ 56
Table 10: Axial Dispersion Relations .............................................................................. 64
Table 11: Dimensionless Parameters Relevant to Bubble Column Mass Transfer ......... 67
Table 12: Summary of Mass Transfer Relations for Dispersed Bubbles in ContinuousLiquids............................................................................................................... 77
Table 13: Ozone Decomposition Rate Constants ............................................................ 84
Table 14: Factors Influencing Bromate Formation........................................................... 90
Table 15: Commonly-used Disinfection Models............................................................. 92
Table 16: Summary of Ozone Inactivation Data (Clark and Boutin 2001) ..................... 93
Table 17: Summary of Ozone Contactor CFD Studies.................................................. 108
Table 18: Comparison of Eulerian-Eulerian and Eulerian-Lagrangian Approaches ..... 117
Table 19: Countercurrent Flow Hydrodynamics Experimental and Numerical Studies 154
Table 20: Countercurrent Flow Peclet Number Relations............................................. 161
Table 21: Mass Transfer Visualization Experiments..................................................... 179
Table 22: Best Fit Parameters ........................................................................................ 204
Table 23: Rate Expressions and Constants, Full Scale CFD Model.............................. 229
ix
LIST OF FIGURES
Figure 1: Inactivation and DBP Formation for a Hypothetical Water............................... 3
Figure 2: Schematic Diagram of a Full Scale Ozone Bubble Contactor ......................... 13
Figure 3: Segregated Flow Analysis Illustration ............................................................. 21
Figure 4: Extended CSTR Method Illustration................................................................ 23
Figure 5: Interrelated Processes in a Bubble Column (adapted from Heijnen and Van'tRiet (1984)) ....................................................................................................... 38
Figure 6: Illustration of Homogeneous and Heterogeneous Bubbly Flow (Camarasa etal., 1999)............................................................................................................ 39
Figure 7: Countercurrent Bubble Column Flow Regimes Schematic Diagram (adapatedfrom Uchida, Tsuyutani et al. (1989) ................................................................ 41
Figure 8: Bubble Rise Velocity and Discharge Coefficient Schematics (Moore 1959) .. 53
Figure 9: Migration of a Bubble Plume to a Wall (Freire et al., 2002) ........................... 59
Figure 10: Migration of Bubble Plumes toward Each Other (Freire et al., 2002) ........... 60
Figure 11: Schematic Diagram of the Two-Film Mass Transfer Model ......................... 68
Figure 12: The Hydrodynamics of the Transport of Ozone from Gas Phase to the BulkLiquid Phase ...................................................................................................... 71
Figure 13: Significant Ozone Disinfection Byproducts (Song et al., 1997; United StatesEnvironmental Protection Agency 1999; von Gunten 2003b) .......................... 86
Figure 14: Bromate Formation Pathways (Song et al., 1997).......................................... 88
Figure 15: Ozone Contactor Design Modifications (Henry and Freeman 1995)........... 101
Figure 16: Murrer, Gunstead et al. (1995) Reactor Schematic ...................................... 103
Figure 17: Reactor Schematic for Cockx CFD Study.................................................... 105
Figure 18: Experimental Reactor Photograph................................................................ 121
Figure 19: Laboratory Bubble Column Schematic Diagram (not to scale) ................... 123
Figure 20: Reactor Schematic Diagram, Scale Drawing ............................................... 124
Figure 21: Scale Drawing of Laboratory Column Bottom ............................................ 124
Figure 22: Conductivity Probe Calibration.................................................................... 126
Figure 23: Typical Tracer Curve.................................................................................... 127
Figure 24: RTD Model Schematic Diagrams ................................................................ 128
Figure 25: Indigo Trisulfonate Structure and Daughter Products.................................. 134
Figure 26: Mass Transfer Visualization Experiment Lighting ...................................... 136
x
Figure 27: Pixel Color Calibration Images .................................................................... 138
Figure 28: Calibration Image Histograms...................................................................... 139
Figure 29: Variation of Absorbance with Indigo Concentration for Indigo ReagentDiluted with Tap Water................................................................................... 140
Figure 30: Pixel Color Calibration Curve...................................................................... 142
Figure 31: Diameter Along which Grid Resolution Study was Performed ................... 150
Figure 32: Gas Volume Fraction Profiles ...................................................................... 151
Figure 33: CFD Model Validation................................................................................. 153
Figure 34: Photographs of Bubble Plume Shapes.......................................................... 155
Figure 35: Flow Visualization – Dye Progress at 30s, 1 min, 1 min 30s and 2 min (theDark Triangle Approximately 1/3 the Reactor Height in Each Image is theGlass Maker’s Manufacturer’s Mark) ............................................................. 157
Figure 36: Experimental Residence Time Distributions (RTDs) for 0 < Qg < 3 L/min 159
Figure 37: Experimental and Predicted Peclet Number................................................. 162
Figure 38: Virtual Tracer Concentration at 20s, 40s and 60s after Step Input .............. 165
Figure 39: Phase Distribution ........................................................................................ 167
Figure 40: Water Velocity Vectors near the Diffuser.................................................... 168
Figure 41: Spatial Variations in Mixing ........................................................................ 170
Figure 42: Typical Intake Configuration for Countercurrent Full Scale Ozonation...... 172
Figure 43: Philadelphia Water Department Pilot Column Phase Distribution .............. 175
Figure 44: PWD Pilot Reactor Intake and Discharge Region Velocity Vectors ........... 176
Figure 45: PWD Virtual Tracer Study ........................................................................... 177
Figure 46: Indigo Dye Decoloration Images ................................................................. 181
Figure 47: Eddy Transport during Ozonation................................................................ 184
Figure 48: Illustration of Well-Mixed Zone and Radially-Averaged Concentration .... 186
Figure 49: Identification of Best Fit Critical Depth....................................................... 192
Figure 50: Mass Transfer Visualization, Qgas = 0.4 slpm, QL = 7.0 lpm, Case A ......... 195
Figure 60: Variation of Entrance Region Length with Gas to Liquid Flow Ratio ........ 206
Figure 61: Variation of Zone 1 Stanton Number with Gas to Liquid Flow Ratio ......... 207
Figure 62: Variation of Zone 1 Peclet Number with Gas to Liquid Flow Ratio ........... 208
Figure 63: Sample Locations ......................................................................................... 211
Figure 64: Predicted and Measured Indigo Dye Concentrations ................................... 212
Figure 65: Image Location, Experimental Images and CFD ......................................... 213
xi
Figure 70: Comparison of CFD and Experimental Indigo Dye ConcentrationData, Q6=0.4 slpm, QL=7.0 lpm ...................................................................... 220
Figure 71: Comparison of CFD and Experimental Indigo Dye Concentration Data,Q6=0.4 slpm, QL=13.5 lpm.............................................................................. 221
Figure 72: Comparison of CFD and Experimental Indigo Dye Concentration Data,Q6=0.7 slpm, QL=7.0 lpm................................................................................ 222
Figure 73: Comparison of CFD and Experimental Indigo Dye Concentration Data,Q6=0.7 slpm, QL13.5 lpm ................................................................................ 223
Figure 74: ACWD Full Scale Reactor Schematic Diagram........................................... 226
Figure 75: Full Scale Reactor CFD Model Schematic Diagram.................................... 227
Figure 76: Gas Volume Fraction Contours, Full Scale Reactor, Vertical Plane............ 230
Figure 77: Gas Volume Fraction Contours, Full Scale Reactor, Horizontal Plane near theSpargers ........................................................................................................... 231
Figure 78: Gas Volume Fraction Contours, Full Scale Reactor, Horizontal Plane at theReactor Mid-height ......................................................................................... 232
Figure 79: Water Superficial Velocity Vectors, Chambers 1 - 5, Full Scale Reactor ... 234
Figure 80: Water Superficial Velocity Vectors, Chambers 6 - 10, Full Scale Reactor . 235
Figure 81: Water Superficial Velocity Vectors, Full Scale Reactor, Horizontal Plane,Chambers 1 – 4, Projection Tangential to Plane ............................................. 236
Figure 82: Water Superficial Velocity Vectors, Full Scale Reactor, Horizontal Plane,Chambers 5 – 10, Projection Tangential to Plane ........................................... 237
Figure 83: Dissolved Ozone Concentration Contours, Full Scale Reactor.................... 238
Figure 84: Bromate Concentration Contours, Full Scale Reactor ................................. 240
Figure 85: Cryptosporidium parvum Density Contours, Full Scale Reactor................. 242
Figure 86: Alternate Lighting Scheme........................................................................... 254
Figure 87: Conservation of Gas Phase Ozone and Aqueous Indigo Dye ...................... 275
Figure 88: Schematic Diagram, Two-Zone Model ........................................................ 283
xii
ABSTRACT
Countercurrent flow hydrodynamics and mass transfer were explored using
computational fluid dynamics (CFD) analyses, tracer studies and a novel mass transfer
visualization technique. In concert, these techniques yielded a comprehensive description
of countercurrent hydrodynamics and mass transfer.
In the laboratory bubble column reactor in which experimental studies were
performed, liquid flowed upward with gas bubbles in the core of the bubble plume and
downward outside the bubble plume near the cylinder walls at all gas flow rates. CFD
predicted a large recirculating flow near the sparger. Well-mixed conditions were
observed in a zone termed the entrance length, located near the sparger. Mass transfer
visualization experiments allowed estimation of the entrance region length. The entrance
region increased as a function of gas flow rate and ranged from a value of about 22% (for
the lowest gas to liquid flow ratio experiment) to nearly 40% (for the highest gas to liquid
flow ratio experiment.
To demonstrate its utility as a design tool or for troubleshooting underperforming
full scale reactors, CFD was used to predict hydrodynamics, Cryptosporidium parvum
inactivation and bromate formation in a full scale reactor. Despite being relatively crude
the CFD model identified flowfield features conducive to bromate formation or
deleterious to C. parvum inactivation. Specifically, in chambers in which ozone is
applied, large recirculating flows were predicted. Water detained in these recirculating
flows have relatively long detention times and contribute to bromate formation in waters
with sufficient bromide content.
xiii
The current study demonstrates that, even in a simple tall right circular
cylindrical bubble column, hydrodynamics plays a major role in contact of ozone with
microorganisms and substances that form bromate. Both experimental and analytical
studies identified significant spatial variations in mixing and mass transfer in the
relatively simple bubble column reactor. These findings indicate that CFD could be more
widely used as a component of pilot scale studies of ozone bubble contactor reactors or in
design of full scale contactors. Given current computer prices and speeds, CFD analysis
is appropriate for plants with capacities which are smaller than the very large capacity
plants for which CFD is presently used.
1
I INTRODUCTION
Thorough, efficient water disinfection requires sustained, uniform contact
between pathogenic organisms suspended in the water and dissolved disinfectant. The
most frequent way of assessing the extent of disinfectant-pathogen contact is through
estimation of “Ct,” where C is the disinfectant residual and t is the contact time between
disinfectant and organisms.
The disinfectant residual is seldom uniform or steady. Chemical disinfectants
react and decay. Mixing of disinfectant with pathogen-laden water may be incomplete.
In ultraviolet disinfection processes, shielding or variations in distance between
pathogens and the UV source may result in non-uniform contact between disinfectant and
microorganisms. To account for spatial and temporal variations in disinfectant-organism
contact and disinfectant residual, estimates for “Ct” are made using conservative
estimates for contact time and disinfectant concentration, such as the time required for
10% of a conservative tracer to exit the reactor in a pulse tracer experiment (T10) and the
disinfectant residual at the reactor discharge or discharge from individual chambers in the
reactor (Lev and Regli 1992a; Lev and Regli 1992b).
Beyond having to account for uneven contact between organisms and disinfectant,
regulatory agencies must also apply safety factors to estimated Ct values to account for
uncertainty in inactivation rate models and for the influence of water matrix constituents
and varying water quality properties on inactivation rate. For example, given the wide
variation in observed Cryptosporidium parvum inactivation rates, disinfection goals up to
1 log-unit higher than desired disinfection goals may be required to ensure actual
2
inactivation is within 95% confidence bounds of predicted inactivation (Finch et
al., 2001).
There are drawbacks to the protective design approach to disinfection process
design criteria described above – disinfection byproduct (DBP) formation and excessive
energy consumption and chemical dosing. Depending on the composition of the water
that is disinfected and the disinfectant used, byproducts that pose chronic human health
risks may be formed during disinfection. Chlorine-based disinfectants produce
trihalomethanes (THMs) and haloacetic acids (HAAs) among other byproducts. THMs
and HAAs are regulated under the Disinfectant and Disinfectant Byproducts rule (US
EPA Office of Water 2001) and numerous community public water treatment facilities
have been out of compliance with these regulations since their promulgation (US EPA
2005).
As will be described in Chapter 2, ozone produces fewer and lower concentrations
of DBPs than chlorine, except in waters high in bromide (Br -). In those waters,
depending on the pH, ammonia concentration, temperature, alkalinity and dissolved
organic carbon concentration, bromate (BrO3-), a suspected human carcinogen, may be
formed. The US EPA’s current maximum contaminant level (MCL) for bromate is 10
g/L.
Microbial inactivation and DBP formation processes occur at the same time scale,
as illustrated in Figure 1. Taking Ct to indicate a level of disinfection, the plot shows
exposure to Cryptosporidium parvum oocysts and bromate commensurate with a range of
disinfection levels. The dashed curve showing reduction in Cryptosporidium parvum is
3
based on an inactivation rate model derived from batch studies of
Cryptosporidium inactivated in filtered water (Finch et al., 2001). The bromate
formation curve was developed based on regression analysis of bromate formation rate
data and is drawn for filtered water with a relatively high (170 g/L) initial bromide ion
concentration (Song et al., 1996). Recalling that the current MCL for bromate is 10 g/L,
achieving a design reduction in Cryptosporidium parvum of 2 logs using only ozone
disinfection is not possible without exceeding the bromate MCL unless steps are taken to
enhance inactivation or retard bromate formation. If appropriate safety factors protective
of microbiological quality are employed, bromate concentration will exceed the MCL by
an even greater amount.
Figure 1: Inactivation and DBP Formation for a Hypothetical Water
4
In chlorine-based disinfection, chemical disinfectant is introduced to the
treatment train as a solution and is mixed with process water prior to introduction to the
disinfection processes. After the disinfectant demand of the raw water is satisfied, the rate
of decay of active forms of chlorine is slow relative to typical retention times in
disinfection processes and the chlorine concentration does not vary significantly in the
reactor. In ozone disinfection, water enters the reactor with no ozone and ozone is
dissolved into process water in early stages of the disinfection process. There is often
significant ozone demand in the early portion of an ozonation process. For example, in a
pilot study of ozonation of Central Arizona Project (CAP) water, identical ozone doses
were applied to two identical cylindrical contactors arranged in series and operating in
countercurrent mode. When the contact time in the cylinders was large (above 7.5
minutes) the increase in ozone residual between the intake and discharge in the second
column was double that of the first column (Nieminski 1990). The rate of decay of ozone
is also significantly higher than that of chlorine disinfectants, especially for water at
temperatures above 20°C or that are slightly basic (Rakness 2005). Thus, ozone
concentration varies more widely than that of chlorine in disinfection processes.
Because the number of pathogens present in treated drinking water is very low,
regulating disinfection processes based on detection of pathogens in reasonably sized
samples is not possible. Rather, the United States Environmental Protection Agency
grants “disinfection credits” for well-operated filtration processes, disinfection and, in
recent amendments to the safe drinking water act, demonstration of high source water
quality and protection (42 U.S.C. 300g-1(b)(7)(C)(iv)). Plants receive “Ct credit” based
on measured or estimated hydraulic characteristics of unit process operations and based
5
on batch kinetic studies of their disinfectant’s decay rate in the plant’s water. Ct
credit for disinfection processes is established based on measurement of disinfectant dose
at the reactor discharge and intermediate locations and on either measured residence time
distributions (RTDs) or using hydraulic models such as continuously stirred tank reactors
(CSTRs) for assessing reactor hydraulics. The Ct required to achieve a desired reduction
in microbial concentration depends on the disinfectant, the microorganism, water
properties (primarily pH and temperature) and constituents, initial microbial density, and
possibly other factors. Log credit awarded by EPA for Cryptosporidium inactivation by
ozone is presented in Table 1.
Table 1: Ct Values for Cryptosporidium Inactivation by Ozone (40 CFR 141.730)
Water Temperature (ºC)Logcredit 0.5 1 2 3 5 7 10 15 20 25
0.5 12 12 10 9.5 7.9 6.5 4.9 3.1 2.0 1.2
1.0 24 23 21 19 16 13 9.6 6.2 3.9 2.5
1.5 36 35 31 29 24 20 15 9.3 5.9 3.7
2.0 48 46 42 38 32 26 20 12 7.8 4.9
2.5 60 58 52 48 40 33 25 16 9.8 6.2
3.0 72 69 63 57 47 39 30 19 12 7.4
The current conservative approach to disinfection is evident in the assessment and
assignment of treatment plant Ct described above. Table 2 provides an overview of the
disinfection/byproduct tradeoff. Source waters carry with them varying loads of
6
pathogenic organisms and chemical compounds and have diverse physical
properties. Given these complexities, establishing an optimal reactor design that provides
sufficient disinfection and minimizes disinfection byproduct formation is clearly a
formidable task that will require significant experimental studies and modeling.
Table 2: Summary of Disinfection Impacts (United States EnvironmentalProtection Agency 1999)
Disinfection parameter Typical impact on pathogeninactivation
Typical impact on DBP formation
Disinfectant type Depends on inactivation efficacy Depends on disinfectant reactivity
Disinfectant strength The stronger the disinfectant, thefaster the disinfection process.
The stronger the disinfectant, thegreater the production of DBPs.
Disinfectant dose Increasing the disinfectant doseincreases the disinfection rate
Increasing the disinfectant dosetypically increases the rate of DBPformation
Type of organism Susceptibility to disinfection variesaccording to pathogen group. Ingeneral, protozoa are more resistantto disinfectants than bacteria andviruses.
None.
Contact time Increasing the contact timedecreases the disinfectant doserequired for a given level ofinactivation
Increasing the contact time with anequivalent disinfectant dose increasesthe formation of DBPs.
pH pH may affect the disinfectant formand, in-turn, the efficiency of thedisinfectant.
The impact of pH varies with DBP.For ozonated water containing bromideion, high pH favors the formation ofbromate ion and low pH favorsformation of brominated organicbyproducts.
Temperature Increasing temperature increasesthe rate of disinfection.
Increasing temperature typicallypromotes faster oxidation kinetics and,hence, increases DBP formation.
Turbidity Particles responsible for turbiditycan surround and shield pathogenicmicroorganisms from disinfectants.
Increased turbidity may be associatedwith increased NOM, which representsan increased amount of DBPprecursors for the formation of DBPswhen disinfectant is applied.
7
Disinfection parameter Typical impact on pathogeninactivation
Typical impact on DBP formation
Dissolved organics Dissolved organics can interferewith disinfection by creatingdemand and reducing the amountof disinfectant available forpathogen inactivation.
Increased dissolved organics willrepresent a larger amount of DBPprecursor for the formation of DBPswhen the disinfectant is applied.
I.1 Objectives and Study Overview
The current study provides detailed quantitative information on the mixing and
mass transfer processes for dissolution of ozone in countercurrent flow and demonstrates
use of a detailed model for design and analysis of ozone bubble contactors. These
detailed measurements and analyses are intended to allow more precise prediction of
ozone mass transfer, microbial disinfection and chemical byproduct formation and can be
used to strike a balance allowing management of acute risk of microbial infection and
management of chronic risks associated with disinfection byproducts.
As described in the following chapter, many mass transfer relations for
dissolution of gases from bubbles have uncertain applicability at conditions differing
from those in which the data from which they were developed were collected.
Specifically, many relations found in the literature were developed for co-current bubble
contactors or are theoretical relations developed without concern over the interactions
between the liquid flow field and bubble plume and their impacts on mass transfer. None
of the mass transfer studies described in the literature review included an assessment of
axial variations in mass transfer. Mass transfer studies and mass transfer relations drawn
from the literature are described in detail in section II.1.1.5. Given the marked difference
8
in the distribution of bubbles and their momentum near the sparger compared
with their distribution and momentum away from the sparger, these axial variations are
expected to be significant and should be explored.
I.1.1 Objectives
The goal of the present work was to quantify the influence of non-ideal
hydrodynamics on mass transfer and contact of dissolved ozone with pathogens in
countercurrent bubbly flow. The objectives of this work were to:
Quantify dispersion (inclusive of axial variations) in a laboratory countercurrent flow
bubble column reactor using experimental residence time distribution studies and
computational fluid dynamic (CFD) modeling and relate the dispersion to reactor
operating conditions and geometry;
Use a novel visualization technique for observing ozone mass transfer (inclusive of
axial variations) in the bubble column and determine whether axial variations in mass
transfer significantly impact the ability of engineers to scale up countercurrent flow
reactors;
Validate a CFD model for ozone mass transfer in countercurrent flow and assess the
accuracy of the mass transfer model in predicting mass transfer in countercurrent
flow; and
Demonstrate the ability of the validated CFD model to simultaneously predict
Cryptosporidium parvum inactivation and bromate formation in a full-scale reactor
9
and identify advantages and disadvantages of CFD compared with design
models currently used in ozone bubble contactor design and Ct credit assessments.
I.1.2 Overview
To achieve these objectives, two sets of experiments were performed and a CFD
model of countercurrent ozone mass transfer, inclusive of relevant chemistry and
microbial inactivation, was developed and exercised. The two sets of laboratory
experiments were
tracer studies performed to quantify mixing and hydrodynamics in countercurrent
gas-liquid flow and
ozone mass transfer visualization studies performed to enable estimation of mass
transfer rate and identify spatial variations in mass transfer.
The CFD model was developed using the commercial CFD code CFX (ANSYS
Inc. 2004) and was validated using data taken in both the tracer studies and mass transfer
visualization studies. Results from CFD studies were compared with those of
experimental studies, providing explanation for trends observed. Finally, a CFD model
was developed and executed for simultaneous prediction of Cryptosporidium parvum
inactivation and bromate formation in a full scale reactor.
10
I.2 When and Why Ozone is Used in Water Treatment
I.2.1 Ozone Use in Potable Water Disinfection
In general, potable water1 disinfectants are strong oxidants and may serve
multiple purposes in the water treatment process. These may include (United States
Environmental Protection Agency 1999):
Inactivation of pathogenic organisms;
Control of aquatic nuisance species;
Oxidation of iron and manganese;
Removal of compounds causing tastes and odors;
Improvement of coagulation (and subsequent filtration);
Removal of color;
Prevention of algal growth in sedimentation basins and filters; and
Prevention of biological regrowth in distribution systems.
Thus, selection of a chemical for water disinfection may be guided by its use in other
processes in water treatment as well as its ability to kill pathogenic organisms.
Chlorine remains the most widely used disinfectant in the United States. As of
2000, The United States Environmental Protection Agency reports that 68.7% of
1 In the remainder of this thesis, all processes will be assumed to be for potable water treatment
and the modifier “potable water” will be omitted.
11
community water systems (systems providing service connections and year-
round service to at least 15 connections or 25 people, inclusive of those required to
disinfect and those exempt) use chlorine downstream of filtration (for those plants
employing filtration) (United States Environmental Protection Agency 2000). This
percentage includes plants using one or more disinfectants in conjunction with chlorine.
Only 0.4% of plants report using ozone downstream of filtration, though 3.5% of
reporting plants use ozone for predisinfection or oxidation upstream of filtration.
However, as American utilities strive to meet disinfection and disinfection
byproduct goals required by the Stage 1 Disinfectants and Disinfection Byproducts Rule
and Long Term 2 Enhanced Surface Water Treatment Rule (LT2SWTR), plants are
assessing ozone disinfection as an alternative, particularly for Cryptosporidium parvum
inactivation and for disinfection byproduct minimization.
I.2.2 Advantages and Disadvantages of Ozone as a Disinfectant
The impetuses for recent increases in the number of U.S. water treatment plants
incorporating ozone disinfection into treatment are concerns over chlorine-resistant
organisms and disinfection byproducts. Specifically, ozone is the only chemical
disinfectant that inactivates Cryptosporidium parvum at doses and contact times
realizable in treatment plants and does not produce the halogen-substitute byproducts
typical of water treated with chlorine. The advantages and disadvantages of ozone
disinfection (compared with other schemes) are summarized in Table 3 (US EPA Office
of Water 1999).
12
Table 3: Advantages and Disadvantages of Ozone as a Disinfectant
Advantages Disadvantages
More effective than chlorine,chlorine dioxide, chloramines forinactivation of viruses,Cryptosporidium parvum andGiardia
Efficient chemical disinfectantrequiring relatively short contacttime
In the absence of bromide, halogen-substitute DBPs are not formed.
Ozone is a strong oxidant andcontrols odor, color and taste
Produces disinfection byproductsincluding products of bromide(primarily bromate), aldehydes,ketones and others.
High capital and operating costs
Ozone is corrosive and toxic
Ozone provides no residual
Ozone decays rapidly at high pHand warm temperatures
I.3 Ozone Contactor Design
I.3.1 Typical Reactor Designs and Design Parameters
Gaddis (1999) lists potential gas-liquid contactors (excluding surface contactors
which would be inappropriate for ozonated water) as bubble columns, stirred vessels, jet
loop reactors and impinging stream reactors. Among these, the bubble column has the
lowest volumetric mass transfer coefficient but offers the advantages of simple design
and operation, high interfacial transfer area (to account for a much higher liquid film
resistance to mass transfer than gas film resistance) and, when well-designed, a greater
propensity toward plug flow hydraulics. Thus, ozone contactors are often bubble
columns. Shah, Kelkar et al. (1982) state that bubble contactors are well suited for slow
liquid phase reactions (such as microbial inactivation by dissolved ozone gas) due to high
13
transport rates between phases, high interfacial area, large liquid holdup and the
absence of moving parts.
A schematic diagram showing typical ozone bubble contactor configuration is
found in Figure 2 (based on Cockx et al., 1999). Countercurrent and co-cocurrent flow
may be encountered, though countercurrent contact between bubbles and liquid is more
common (Rakness 2005). Industrial ozone bubble contactors are typically on the order of
4 m tall and employ baffling as shown in Figure 2 to promote uniform contact between
the phases and distribution of ozone in the untreated water. Off gas from industrial
bubble contactors is collected and either destroyed or recycled and reinjected into the
water.
Waterinlet
Outlet
Ozonated air
Waterinlet
Outlet
Ozonated air
Figure 2: Schematic Diagram of a Full Scale Ozone Bubble Contactor
The bubble contactor design features that determine contactor performance and
over which engineers have control are (Do-Quang et al., 2000):
Contactor geometry;
Gas/water flow rates:
14
Gas/water flow ratio; and
Diffuser positions.
The choice of these design and operating parameters determines bubble contactor
performance and is manifested in gas holdup distribution, liquid phase mixing, mass
transfer coefficients, bubble size distribution and coalescence (Sanyal et al., 1999).
Geometric features of contactors demonstrated to significantly improve hydraulic
performance (increase the ratio of T10 to hydraulic residence time) are addition of baffles
(especially double baffles), use of spargers that produce fine bubbles, and uniform
distribution of spargers along the contactor bottom (Henry and Freeman 1995; Do-Quang
et al., 2000). Design features that have shown only minor influence on reactor hydraulics
performance are addition of corner fillets and wall foils.
I.3.2 Reactor Design and Scale-up
With the possible exception of CFD analyses, there are no models or fundamental
theories capable of a priori, dependable prediction of liquid phase mass transfer
coefficients or gas phase holdups for multiphase flow reactors (Nauman 2001). Factors
such as non-ideal reactor hydrodynamics, variations in liquid or gas composition and
quality, and transient operation influence mass transfer rate. So full scale ozone bubble
contactor reactor designs are based on measurements taken in bench scale semi-batch or
batch experiments performed in well-stirred reactors or on measurements in continuous
flow pilot systems.
To the extent possible, engineers are advised to design pilot and bench scale
reactors that physically resemble full scale reactors (Langlais et al., 1991), giving rise to a
15
chicken and egg dilemma. Scale-up of semi-batch systems can be done
effectively – Rakness (2005) reports nearly identical predicted and realized performance
for a full scale ozone contactor designed based on semi-batch data. One possible
explanation for this agreement is that the chambers in the full-scale contactor perform as
continuously stirred tank reactors (CSTRs) and that the hydrodynamics closely resemble
those in semi-batch experiments. The positive side of this agreement is that the full scale
contactor achieved design goals. The negative side is that, if the chambers are behaving
as CSTRs, ozone transfer and inactivation are less than they would be if the contactor had
been designed with hydraulics closer to plug flow.
Often, in pilot studies gas phase ozone concentration is measured only at the
reactor intake and in the off-gas and ozone mass transfer is quantified via the transferred
dose or the transfer efficiency (100% transfer dose/applied dose) (Langlais et al., 1991;
Rakness 2005). Because ozone contactors are invariably designed with relatively low gas
to liquid flow ratios, transfer efficiency is almost always very high (> 95%). Commonly,
design engineers simply assume that transfer efficiency of typical bubble contactors is in
the range 90% to 95% (Schulz et al., 2003). Such gross mass transfer data and
assumptions provide no information on where in the reactor the mass transfer occurs and
provide no guidance on the optimal liquid phase depth, despite the goal of setting full
scale reactor depth to ensure high transfer efficiency and minimize ozone production
costs (Langlais et al., 1991).
16
I.3.3 Ct Credit
As described above, utilities demonstrate compliance with water disinfection
regulations by obtaining “Ct” credits based on design and operation of bubble contactors,
not through direct measurement of reduction in microbial loads in the process stream. A
description of how Ct is calculated follows. This discussion is important because
meeting Ct requirements is the primary design goal for engineers designing ozone bubble
column reactors. For the work presented in this dissertation to be of practical use in the
water treatment industry, it must be applicable within the framework of the current
regulatory system or it must present alternative methods for ensuring adequate
disinfection.
The US EPA has approved assessment of Ct in ozone bubble contactors via one of
four prescribed models (described below) or via a site specific evaluation (US EPA
Office of Water 2003; Rakness 2005). The models allowable for claiming Ct credit in
ozone bubble contactors are:
The T10 method,
segregated flow analysis (SFA);
completely stirred tank reactor (CSTR) analysis; or
extended CSTR analysis.
Guidelines for selection of Ct calculation method from EPA’s guidance for
compliance with the Long Term 2 Enhanced Surface Water Treatment Rule
(LT2ESWTR) are presented in Table 4.
17
Table 4: Guidelines for Selection of Ct Calculation Method
Sectiondescription Terminology
Method forcalculating loginactivation Restrictions
Chambers where ozone is added
First chamber First dissolutionchamber
No log inactivationcredit isrecommended
None
OtherChambers
Co-current orcounter-currentdissolutionchambers
CSTR method in eachchamber w/ ameasured effluentresidual concentration
No credit given to a dissolutionchamber unless detectable ozoneresidual is measured upstream of thechamber
Reactive Chambers
3consecutivereactivechambers
Extended CSTRzone
Extended CSTRmethod in eachchamber
Detectable ozone residual should bepresent in at least 3 chambers inzone, measured via in-situ sampleports. Otherwise, apply CSTRmethod individually to eachchamber with a measured O3
residual
No
trac
erd
ata
< 3Consecutivechambers
CSTR reactivechambers
CSTR method in eachchamber with ameasured ozoneresidual concentration
None
Chambers where ozone is added
First chamber First dissolutionchamber
No log inactivationcredit isrecommended
None
OtherChambers
Co-current orcounter-currentdissolutionchambers
T10 or CSTR methodin each chamber
No credit is given to a dissolutionchamber unless a detectable ozoneresidual is measured upstream of thechamber
Reactive chambers
3consecutivereactivechambers
Extended CSTRzone
Extended CSTRmethod in eachchamber
Detectable ozone residual should bepresent in at least 3 chambers inzone, measured via in-situ sampleports. Otherwise, apply the T10 -CSTR method individually to eachchamber with a measured O3
residual
Wit
htr
acer
dat
a
< 3Consecutivechambers
CSTR reactivechambers
CSTR method in eachchamber with ameasured ozoneresidual concentration
None
18
The compliance guidance for the LT2ESWTR has been withdrawn
pending revision, though the draft guidance (US EPA Office of Water 2003) is referenced
in this dissertation. The LT2ESWTR allows calculation of Ct using the extended CSTR
method (described below) in addition to the methods allowed under the Surface Water
Treatment Rule (SWTR) (US EPA Office of Drinking Water 1991).
I.3.3.1 The T10 Method
In the T10 method, conservative estimates for the residence time of fluid elements
in the reactor and the average ozone concentration in the elements during their residence
are made and Ct is the product of the estimates. T10, the time required 10% of a
conservative tracer introduced as a pulse at the reactor inlet to exit the reactor, has been
shown to provide a conservative estimate of the time fluid elements spend in a reactor,
whether flow in the reactor approaches that in a CSTR or that of an advection-dispersion-
reaction model (Lev and Regli 1992b). Since the ozone concentration varies from
chamber to chamber in a multi-chamber reactor (such as the one depicted in Figure 2), it
is necessary to estimate the T10 for individual chambers separately. In the absence of
tracer data for individual chambers, it is assumed that the T10 of individual chambers
scales with the overall system T10 according to
system,10
system
subunitsubunit,10 T
V
VT
(1)
where subunitV is the volume of the subunit and systemV is volume of the overall system.
According to the authors, equation 1 provides a reasonable estimate of subunit T10 for
subunits whose volume is less than 50% the total reactor volume.
19
Because ozone undergoes autodecomposition in water, ozone
concentration is not constant in contactors and the average ozone concentration in
subunits of the reactor must be estimated for use in Ct calculations. The mode of
operation (countercurrent two-phase flow, co-current two phase flow or reactive segment
[with no ozone application]) in a given reactor subunit dictates the way the average ozone
concentration is calculated. It is assumed that, because of ozone demand and decay, no
significant ozone residual is achieved in the first chamber of an ozone bubble contactor in
which ozone is applied. In subsequent chambers, the following guidelines apply (Lev
and Regli 1992a):
segmentsReactive
operationCocurrentor
32operation;rentCountercur
chamberndissolutioFirst0
out
outinout21
out
avg
C
CCC
ssCC (2)
In equation 2, Cavg is the average ozone concentration in a subunit, Cout is ozone
concentration at the subunit discharge, Cin is the ozone concentration at the subunit inlet
and s is a safety factor. When ozone decomposition rate is high, the safety factor
approaches the value 3; when decomposition rate is low, it approaches 2.
I.3.3.2 CSTR Analysis
The CSTR analysis (described below) is appropriate for
reactors whose flow approaches that of a CSTR,
reactors with only one chamber and for which T10 / HDT < 0.33 and required
inactivation level for Giardia greater than or equal to 2.5 logs, and
20
reactors for which there are no tracer data (U.S. EPA Office of Drinking
Water 1991).
Assuming disinfectant and microorganisms are homogenously distributed within a
reactor chamber and that inactivation of microorganisms is first order with respect to
microorgansism concentration and disinfectant concentration (Chick kinetics), the Ct that
achieves a survival ratio of 0NN (concentration of surviving organisms divided by
concentration of organisms introduced to the chamber) is given by
0
0
303.2
1HDT
NNk
NNC
(3)
In equation 3, HDT is the theoretical hydraulic detention time (chamber volume
volumetric flow rate) and k is the inactivation rate constant (assuming first order kinetics
with respect to microorganism density and disinfectant concentration) for the
microorgansism of interest. At present, the two organisms believed most resistant to
disinfection are Giardia and Cryptosporidium and Ct is calculated for one or both of
those organisms. The inactivation rate constant may be determined via batch kinetic
studies (the preferable method) or drawn from tables of inactivation rate constants
published by the EPA.
I.3.3.3 Segregated Flow Analysis
In the segregated flow analysis (SFA), it is assumed that the inactivation achieved
in a reactor is proportional to two probabilities: the probability that a microorganism
remains in the reactor for a specified time and the probability that the microorganism is
21
inactivated if exposed to disinfectant for the specified time. The segregated
flow model is illustrated in Figure 3.
12
3
4
1
2
3
4
t
Width of bars is proportional to fraction of flowthrough the segment
Figure 3: Segregated Flow Analysis Illustration
The probability distribution for water (and microorganism) residence times, E(t),
is determined via tracer studies and residence time distribution analyses (Danckwerts
1953; Haas et al., 1997). The probability of inactivation over a time period, t, is
calculated using a modified form of Chick’s law (Trussell and Chao 1977):
kCt
N
N 100
(4)
Note that in equation 4 that the ozone residual concentration, C, is assumed constant with
respect to time. The EPA’s guidance does not provide explicit instructions on the value
of ozone concentration for use in equation 4.
The overall probability of organism survival is then
n
i
Ctk
iitE
N
N
10
10 (5)
22
where n is the number of segments into which the flow was divided. Equation
5 may be used to determine the concentration, C, required to achieve a desired level of
disinfection.
I.3.3.4 Extended CSTR Analysis
In the extended CSTR method, three or more consecutive reactive chambers
(chambers without ozone addition) can be analyzed as consecutive CSTRs (US EPA
Office of Water 2003). In the ozone bubble contactor shown in Figure 4 (based on the
example of the extended CSTR method provided by Rakness (2005)), the reaction zone
over which the extended CSTR method may be used to estimate inactivation is comprised
of all the chambers downstream of chamber 1 (in which ozone is applied). Each of the
chambers is treated as a CSTR. Three sample points, S1, S2 and S3 are shown. The
ozone residual is measured at each o those sample points and used in estimation of the
ozone decay rate and average residual in each chamber. The advantages of the extended
CSTR method are that it requires very little experimental data and that it accounts for
ozone decay more systematically than the other Ct analyses.
The ozone decay rate, k*, in the reactor is estimated based on the difference in
ozone residual measurements made at sample ports 1 and 2 and between sample ports 1
and 3. Sample location one should be at least one chamber downstream of the discharge
of a chamber in which ozone is applied. This ensures that most of the ozone demand has
been exerted and measured differences in ozone concentration are due to
autodecomposition.
23
1 2 3 4 5 6 7 8
S1
S2 S3
Reaction zone
Reaction zone hydraulic detention time
Ozo
nere
sid
ual
(mg
/L)
Figure 4: Extended CSTR Method Illustration
Assuming all chambers are CSTRs, the decay rate between sample locations i and
j is given by
1HDT
1
*
jin
j
i
ji
ji
jiC
Cnk (6)
where *jik is the apparent ozone decay rate based on measurements i and j, ni-j is the
number of chambers between sample points i and j, (HDT)i-j is the net theoretical
hydraulic detention time between sample points i and j, and Ci and Cj are the ozone
24
residual concentrations measured at sample points i and j. Equation 6 is
evaluated between sample points 1 and 2 and between sample points 1 and 3. The
average decay rate, *avgk , is the average of *
21k and *31k , provided neither value differs
from the average by more than 20%.
The ozone concentration at the inlet to the reaction zone is estimated based on the
concentrations measured at the three sample points. First, an inlet concentration is
estimated based on the average decay constant and the measured ozone concentration at
each sample point:
10
10
10*11in, 1
n
avgQn
VkCC (7)
20
20
20*2in,2 1
n
avgQn
VkCC (8)
30
30
30*3in,3 1
n
avgQn
VkCC (9)
In equations 7-9, Cin,i is the reaction zone inlet concentration estimated based on the
concentration measured at sample location i, Ci is the concentration measured at sample
location i, iV 0 is the reactor volume between the reaction zone inlet and sample location
i, in 0 is the number of chambers between the reaction zone inlet and sample location i,
and Q is the volumetric flow rate. Concentration at the intake to the reaction zone is then
3
in,3in,2in,1 CCCCin
(10)
25
The characteristic concentration for each chamber is calculated via the
expression
in
i
iavg
ini
nk
CC
0
0
0* HDT1
(11)
and the Ct for each chamber is the product of the hydraulic detention time and the
characteristic concentration for that chamber. The overall Ct for the reaction zone is the
sum of the Cts of the chambers in the reaction zone.
I.3.4 Roles for CFD within the Regulatory Framework
The models used to determine regulatory compliance are low-fidelity (zero-
dimensional) and were developed to be easy to use and very conservative in their
estimation of level of disinfection. Notwithstanding the presence of a CFD approach in
the current regulation, there are several roles CFD might play in the ozone contactor
design and benchmarking processes.
First, CFD models can provide detailed information on hydrodynamics that
cannot be deduced from tracer studies or from sampling from a small number of positions
in the reactor. This includes the situation where the reactor does not yet exist. Where
tracer studies might identify that short-circuiting is occurring, CFD could be used in
determining where the short-circuiting occurs. Where sampling such as that performed in
the extended CSTR analysis can provide information on ozone concentration at strategic
points, CFD can be used to predict concentration profiles anywhere in the reactor and
more accurately quantify the variations in concentration throughout the reactor. CFD
26
might be used to inform the choice of sample locations, enabling engineers to
avoid regions of backflow or other regions where the concentration might not be
representative of reactor performance.
Second, CFD could be used as a component of the design process, supplementing
and guiding the more intelligent conduct of expensive and time-consuming
experimentation. If, through tracer analysis or other means, engineers determine a
reactor has an unusually short T10, they may opt to alter the reactor design to improve
hydraulics and achieve a higher Ct. A validated CFD could be used to predict
performance of reactors with modifications such as baffle additions, inlet or discharge
reconfigurations or modified sparger placement.
Finally, as is demonstrated in the dissertation, CFD can be used for modeling
multiphase reacting flows. This ability will enable design engineers to progress beyond
models in which the ozone transfer efficiency is assumed. Improved modeling and
understanding will yield reactor designs that improve bubble-liquid contact and mixing
and promote more uniform ozone concentration in the process water.
I.4 CFD in Water and Wastewater Treatment Operations Analysis
Computational fluid dynamics (CFD) is being used more frequently in the water
treatment and wastewater treatment engineering due to improvement in commercially-
available CFD codes (especially improved physics and chemistry submodels) and
because personal computers now have sufficient speed and memory to permit modeling
of realistic water treatment processes.
In water treatment, CFD has been used to
27
assess design modifications for improved clarifier performance (Adams and
Rodi 1990; Lyn et al., 1992; Zhou et al., 1994; Brouckaert and Buckley 1999; Craig
et al., 2002),
simulate and troubleshoot flocculation processes (Ducoste and Clark 1999; Lainé et
al., 1999; Liu et al., 2004),
model the performance of a static mixer (Jones et al., 2002),
simulate hydrodynamics and microbial inactivation in pilot and full scale chlorine
contact chambers (Falconer and Ismail 1997; Wang and Falconer 1998; Greene et al.,
2001),
simulate multiphase flow in flotation processes (Sarrot et al., 2005);
assess ozone contactor hydraulics, mass transfer and microbial inactivation (Henry
and Freeman 1995; Murrer et al., 1995; Cockx et al., 1999; Do-Quang et al., 1999;
Cockx et al., 2001; Huang et al., 2002; Ta and Hague 2004) and
assess mixing in water storage tanks and reservoirs (Ta and Brignal 1998).
This list of applications will certainly grow as researchers develop and validate CFD
models for water treatment applications and the environmental engineering community
realizes benefits from CFD studies.
CFD has allowed engineers to perform relatively inexpensive testing and can be
used to assist in reactor scale-up and design (e.g., in design of a UV disinfection reactor
(Valade et al., 2003)). As noted in a previous study (Brouckaert and Buckley 1999),
treatment processes in water and wastewater treatment plants are often carried out in
28
large vessels prone to non-uniform flow or other non-ideal flow characteristics.
Examples of non-ideal processes that may take place in typical unit operations are:
Short circuiting or dead zones in reactors;
Poor mixing of reagents (e.g., coagulants) in flow streams;
Inefficient settling in clarifiers operated at loadings different from design values;
Stratification in membrane reactors;
Stratification or short-circuiting in reservoirs and storage tanks.
Experimental determination of flow conditions in water and wastewater reactors and
appurtenances is costly given the size of reactors and the likelihood that units would have
to be taken off-line to facilitate measurements. Thus, CFD appears to meet a need
currently not addressed in the water treatment industry.
I.5 Need for the Current Study
As illustrated in the literature review below, current design methodology for
ozone contactors relies on simplified, calibrated models that are applicable over a
relatively narrow range of reactor designs and operating conditions. So the current study
was formulated to assess the ability of CFD to model operation of ozone bubble
contactors accurately, inclusive of all significant hydrodynamics, chemistry and biology,
using only submodels for turbulence (mixing), mass transfer, chemistry and microbial
inactivation that are independent of reactor geometry or operating conditions. Such a
capability would be a great benefit to engineers assessing the performance of pilot scale
29
reactors and designing full-scale reactors in which hydrodynamics may differ
significantly from those encountered at the pilot scale.
Despite an extensive literature related to bubble columns, relatively few studies
have been conducted on the behavior and modeling of countercurrent bubble flows and
the performance of countercurrent bubble columns and even fewer have considered mass
transfer; to date the majority of published studies on bubble contactor operation have
focused on hydrodynamics and have analyzed columns of bubbles injected into a non-
flowing liquid column or cocurrent flow. The work performed in this study was
developed to advance the state of CFD analysis of bubble columns by adding the
complexities of countercurrent flow, mass transfer, reaction and microbial inactivation.
These additions are significant since the objective of a bubble column is to produce
efficient mass transfer between phases and contact between disinfectant and pathogenic
organisms and because many industrial bubble columns are run in countercurrent mode.
Just as a systematic study has been made of CFD submodels for momentum
exchange between phases, so should there be a systematic study of mass transfer models.
The CFD studies identified in the literature survey of this proposal present no strong
justification for their selection of mass transfer submodel and the scientific community
will benefit from a thorough review of the sensitivity of CFD simulations to choice of
mass transfer relation and guidance in selecting a relation for a given design and
operating condition.
30
I.6 Significance of the Proposed Work
I.6.1 Advancement of Knowledge
The current work is intended to yield three important contributions to the
technical literature:
Rigorous verification and validation of CFD countercurrent hydrodynamics and mass
transfer submodels for ozone bubble contactor simulations;
Detailed experimental and modeling investigation of interphase ozone mass transfer
and mass transfer models; and
Demonstration of simultaneous prediction of microbial inactivation and bromate
formation with a CFD model that does not need to be “calibrated” with experimental
data.
The majority of bubble contactor CFD studies published to date have entailed modeling
hydrodynamics of bubble columns with either stagnant water or cocurrent flow. In the
few studies published that included interphase mass transfer, countercurrent flow and
microbial inactivation, researchers have not provided justification for their selection of
bubble drag, interphase mass transfer or microbial inactivation models. Validation of
submodels is an important step in demonstrating the utility of CFD in design of water
treatment unit operations and will boost the confidence of the water utility community in
CFD analyses.
Since bubble column hydrodynamics has been addressed in other studies, the
mass transfer studies proposed herein will likely yield the greatest immediate benefit to
31
the scientific community. As described in detail below, mass transfer in bubble
columns is complex and varies with water depth within a given reactor operating at
known water and gas flow rates. The experimental work described below was designed
to allow visualization of the mass transfer process and yield quantitative and qualitative
data on the influence of phase distribution and mixing on the mass transfer rate. The
experiments were novel and, arguably, were a significant improvement over pilot reactor
mass transfer studies that have been performed in the past.
The CFD simulations of interphase mass transfer provide further details on
interphase mass transfer physics and, most important, demonstrate that CFD is a better
design tool than currently-used models and scale-up laws. CFD offers two benefits to the
other approaches:
Use of first principles in development of the model and
characterization of the problem in sufficient detail to account for the influence of
reactor geometry on reactor performance.
These benefits allow CFD to be used in more phases of the design process, even
including the design of pilot facilities. Whereas lower-fidelity models such as the one-
dimensional advection-dispersion-reaction model and completely stirred tank reactor
(CSTR) model require calibration and cannot be used for reactors whose geometry differs
from those to which the models were calibrated, CFD may be applied to any geometry.
Prediction of microbial inactivation and bromate formation in a full scale reactor
with a CFD model is significant both because it will be the first such study in a published
32
work and because it will demonstrate a methodology for achieving an illusive
public health goal – balancing acute microbial risk with long term risk from DBP
consumption.
A final, incremental advancement in scientific knowledge is provided in
simulation of microbial inactivation in continuous flow reactors. The microbial
inactivation modeling performed builds upon the work performed by Greene (2003).
However, this work further develops a procedure for including microbial inactivation in
CFD simulations of continuous flow reactors and may expose alternatives or
modifications to the Ct approach to reactor design leading to reduced deleterious
byproduct formation.
I.6.2 Value to Industry
Compared with engineers from other disciplines, environmental engineers have
been slow to adopt CFD as a design and analysis tool, though in the past 3-4 years the
number of publications of CFD studies related to water and wastewater unit operations
has increased dramatically. Validation and experience with CFD such as demonstrated in
this dissertation should increase the confidence of the engineering community in CFD
analyses and demonstrate the utility of CFD to water utilities choosing between
experimental programs and CFD studies. CFD cannot replace careful experimentation in
water treatment. It can, however, be used in concert with experimentation to shorten
design cycle time, improve design of extant reactors, troubleshoot underperforming
reactors and explore novel reactor designs. This study can act as another stone in the
33
foundation of studies that will make CFD a more attractive tool to
environmental engineers.
An additional value to industry of the current work is improved understanding of
ozone transfer in bubble contactors. According to calculations and experiments made in
this study and the observations made in past studies (Mariñas et al., 1993), the most
intense ozone transfer in bubble column reactors often takes place over a relatively small
vertical portion of the reactor. Most ozone contactors are designed for nearly 100%
ozone mass transfer efficiency (i.e., 100% of the applied dose transfer to the water). This
design philosophy is necessitated by the expense of generating ozone and a lack of design
relations capable of accurately predicting mass transfer rates in arbitrary geometries. The
insights into mass transfer drawn from the work reported in this thesis may suggest
reactor designs that are consistent with the processes occurring in countercurrent flow
mass transfer and achieve acceptable ozone transfer efficiencies with reduced bromate
formation.
The proposed work can contribute to the development and evaluation of the
models the U.S. EPA current allows for utilities wishing to claim inactivation credit for
ozone bubble contactors. Current guidelines do not allow inactivation credit for the first
chamber in which ozone is introduced into a bubble contactor. The assumption is that
ozone demand and decay in the first dissolution chamber are so high that no significant
accumulation of dissolved ozone occurs. CFD analyses, as performed in this study, could
allow detailed knowledge of ozone distribution in the first dissolution chamber and
assessment of this guideline. In addition, CFD calculations can be compared with results
34
from CSTR, extended CSTR and segmented flow models of ozone bubble
contactors. These comparisons will provide information that will help utilities make
appropriate choices for modeling to claim inactivation credit and will provide
information to U.S. EPA on whether the segmented flow model is appropriate for ozone
bubble contactors and how best to apply it.
35
II LITERATURE SURVEY
This chapter surveys studies of bubble column reactor hydrodynamics and
performance, ozone disinfection and byproduct formation, modeling studies apropos to
ozone bubble contactors and ozone bubble column reactor design and scale up.
First, a description of phenomena occurring in bubble column reactors in general
and ozone bubble contactors in specific is presented. Next, models for the physical and
chemical phenomena occurring in ozone bubble contactors are reviewed. This review is
merited since these models are employed in CFD simulations and because CFD
simulations may provide a means to estimate some of the parameters commonly used in
reactor design.
Significant processes that occur in diffused ozone bubble column reactors are:
Gas injection and bubble dynamics
o Introduction of gas into liquid stream
o Evolution of bubble shape and acceleration to terminal velocity
o Bubble breakup, collision and agglomeration
Mixing
o Large length scale liquid phase turbulence related to the reactor intake, discharge
and geometry and exchange of momentum between the bubble plume and liquid
outside the bubble plume
o Small length scale liquid phase turbulence related to dissipation of turbulence and
hydrodynamics of bubble wakes
36
Mass transfer
o Dissolution of gaseous ozone molecules through chemical and physical barriers at
the bubble surface and into the liquid phase
o Diffusion (penetration) of dissolved ozone into liquid adjacent to the bubble
surface
o Exchange of liquid at the bubble surface with liquid from the bulk liquid phase
o Exchange of ozone-rich liquid in the bubble plume with ozone-poor liquid outside
the bubble plume.
Chemical reaction and microbial inactivation
o Ozone demand
o Ozone decay
o Bromate and disinfection byproduct (DBP) formation
o Microbial inactivation.
Studies that provide insight into or quantification of these processes are
summarized below. The data and relations presented are drawn from a rich literature on
bubble column reactors. The vast majority of published studies describe performance of
pilot scale cylindrical bubble column reactors operated in either co-current mode (with
the liquid and gas phases flowing in the same direction) or with non-flowing liquid phase.
Because bubble column reactor performance is strongly dependent on column geometry
(especially diameter to height ratio) and operating conditions (especially gas to liquid
37
volumetric flow ratio), the studies summarized below should be applied to
countercurrent bubble column flow only after consideration of mode of operation and
scale.
After description of phenomena occurring in diffused bubble ozone contactors,
models that have been developed for bubble column reactors and ozonation processes are
summarized. Models differ in spatial dimensionality (0, 1 2 and 3 dimensional models),
type (empirical, stochastic and deterministic) and in the physics, chemistry and biology
included. Particular attention is paid to the application of computational fluid dynamics
(CFD) to bubble column reactors and to ozone bubble contactors.
II.1 Bubble Column Reactor Phenomena
Figure 5 is an illustration of the interrelated processes that occur in bubble
columns (Heijnen and Van't Riet 1984). As indicated in the diagram, flow and mass
transfer in bubble columns are related to the choice of sparger, liquid properties, gas
properties, bubble column operating conditions and bubble column geometry. Bubble
columns may be operated in co-current mode (with bulk gas and liquid flows in the same
direction), countercurrent mode (with liquid and gas phase bulk flows in opposite
directions) and without net liquid flow. Note that, even in the absence of net liquid flow,
bubbles produce large- and small-scale liquid motions in bubble columns. Dispersion,
hold-up and mass transfer differ significantly for bubble columns undergoing these three
modes of operation.
For all three modes of operation, changing the ratio of gas flow rate to liquid flow
rate changes the interactions between bubbles and between the phases. For relatively low
38
gas flow rates and liquid flow rates less than the bubble terminal rise velocity,
bubbles tend to be small, non-interacting and dispersed and flow is in the “ideal bubbly
flow” or “dispersed flow” regime. In this regime, bubbles tend to be monodisperse and
there is not significant breakup or coalescence of bubbles.
Figure 5: Interrelated Processes in a Bubble Column (adapted from Heijnen andVan't Riet (1984))
II.1.1 Countercurrent Two-phase Flow Modeling
Depending upon the relative velocity of the phases in a countercurrent bubble
column, three flow regimes are possible: bubble flow (also called ideal bubbly flow);
39
churn turbulent flow; and bubble down flow (Uchida et al., 1989). Bubbly flow
is characterized by a narrow, monomodal distribution of bubble diameter and negligible
break-up or coalescence (Olmos et al., 2003). Churn turbulent flow and the transition
region between bubbly flow and churn turbulent flow are also termed heterogeneous
flow. Homogeneous and heterogeneous bubble flows are illustrated in Figure 6. Other
regimes (churn turbulent and slug flow) may be encountered at very high gas flow rates,
but are not depicted in Figure 6 because it is unlikely they would be encountered in
typical ozone contactor bubble column operation.
Figure 6: Illustration of Homogeneous and Heterogeneous Bubbly Flow (Camarasaet al., 1999)
Bubble column flow regimes are shown schematically in Figure 7 (adapted from
Uchida, Tsuyutani et al. (1989)). The trends depicted in Figure 7 are based on
40
experimental data collected for a single bubble column (4.6 cm inner diameter)
operated in countercurrent mode over a range of gas to liquid flow ratios. Data were
collected for air bubbled into water and glycerol solutions of 5%, 10% and 15%.
The transition from bubble flow (ideal bubbly flow) to churn turbulent flow
occurred in a well-defined band (depicted with dashed lines) of gas-liquid flow ratios for
the liquids studied. The transition from bubble flow to bubble downflow was, not
surprisingly, strongly dependent on liquid composition (and surface tension, which
influences bubble shape and surface mobility) and temperature. The family of solid
curves drawn on Figure 7 indicates the transition associated with the liquids tested.
Transition occurred earliest (at the lowest gas flow rate) for the 15% glycerol solution
and latest (at the highest gas flow rate) for the lowest-temperature water tested.
Based on their results, Uchida, Tsuyutani et al. determined that the boundary
between churn turbulent flow and other flow regimes was insensitive to the composition
and properties of the liquid phase and dependent mainly on reactor design and choice of
sparger. The boundary between ideal bubbly flow and bubble down flow was strongly
dependent on the composition of the liquid phase. This may be due to differences in
properties in the liquid phase and/or differences in bubble properties and tendency to
coalesce. Lockett and Kirkpatrick (1975) suggest that the transition from ideal bubbly
flow to churn turbulent may be related to liquid circulation due to spatial variations in gas
phase holdup at a given axial location or the presence of large bubbles. Flooding (not
shown on Figure 7) is unlikely for the flow conditions typically encountered in bubble
41
columns and likely plays no role in the transition from ideal bubbly flow to
churn turbulent flow.
Figure 7: Countercurrent Bubble Column Flow Regimes Schematic Diagram(adapated from Uchida, Tsuyutani et al. (1989)
Ruzicka, Drahoš et al. (2001) quantified the effect of liquid depth and bubble
column diameter (for cylindrical columns) on the critical gas hold-up (column volume
occupied by gas divided by column volume) at which transition from homogeneous
bubbly flow to heterogeneous regime occurs. Although their work was done in bubble
columns with stagnant liquids, it can be assumed that transition from ideal to churn
turbulent flow in countercurrent bubble columns is also dependent on column diameter
42
and liquid depth. In general, the authors found that increasing the column
diameter caused transition to heterogeneous bubble flow at lower void ratios and
increasing liquid depth in the column caused transition to heterogeneous bubble flow at
lower void ratios. In reviewing bubble column transition literature, Ruzicka et al. found
the effect of column diameter on transition was due to turbulence scale, intensity of
circulations, back-mixing, dispersion, wall friction and turbulent viscosity. The
dependence of liquid depth on critical void ratio was attributed to the relative importance
of the flow regions at the top and bottom of the column (compared with the region in the
middle of the column).
As described by Camarasa, Vial et al. (1999), the behavior and modeling of
liquid-solid two phase systems is significantly different from that of gas-liquid two-phase
systems. In gas-liquid two-phase systems, the properties of the dispersed phase (bubble
shape and size, distribution of bubbles in the column, influence of bubbles on each other)
depend on reactor geometry and operating conditions and the physico-chemical
properties of the continuous phase. According to Camarasa, this coupling of dispersed
phase properties with continuous phase behavior precludes a priori bubble column
reactor design given current knowledge of processes in bubble columns. Based on these
considerations, hydrodynamics and mass transfer are likely fundamentally different in
cocurrent bubble columns, countercurrent bubble columns and bubble columns in which
gas is introduced into non-flowing liquids. Specifically, liquid-phase dispersion,
circulation in the bubble column and bubble breakup and coalescence differ significantly
between the column configurations.
43
Cocurrent bubble column flow has been studied in greater depth than
counter current bubble column flow. For example, Deckwer, Burckhart et al. (1974)
performed cocurrent flow experiments in bubble columns of 15 cm and 20 cm and
employing different spargers. The experiments were conducted with air bubbled into tap
water and various salt and molasses solutions. The primary objective of these studies
was development of relations to predict oxygen mass transfer. Based on measured gas
phase holdup and analysis of samples taken at an unspecified number of axial locations in
the reactor, the authors concluded that, for the cocurrent configuration employed,
there was little or no axial variation in oxygen mass transfer rate in the columns;
the mass transfer rate was influenced more by sparger type than column dimensions;
for the liquids studied, the mass transfer rate, kLa, varied roughly linearly with gas
velocity
addition of electrolytes to the solution appeared to reduce bubble size (increasing
specific surface area, a) but decrease mass transfer coefficient, kL, resulting in a
slightly lower overall mass transfer rate.
II.1.1.1 Bubble Size and Interfacial Area
The shape of bubbles and the drag they impart on the water depends upon the
water surface tension (which may, in turn, depend on the concentration of impurities in
the feed water), the manner in which they are injected into the water (gas flow rate and
diffuser type), the flow rate of the water column, and the temperature. Moore (1959)
44
suggests that bubble shape is the dominant feature in determining bubble drag
and rise velocity in the flow regimes normally encountered in bubble column flows.
Bubble size is largely a function of sparger type, aqueous phase properties and gas
velocity. Though it is convenient to work with a characteristic bubble diameter in
performing calculations, it should be remembered that there is variation in bubble
diameter at a given axial station in a contactor and that bubbles change size in the
contactor, often having significantly different average diameter near the sparger
compared with mean diameter in the rest of the bubble column.
The two processes integral to determining bubble size are injection and
coalescence. Injection of gas into a liquid column may be via nozzles, porous discs or
two-phase injectors (Heijnen and Van't Riet 1984). The type of sparger largely
determines the size of bubble introduced to the liquid while the behavior and possible
coalescence of bubbles in the liquid column is mainly a function of aqueous phase
properties. Pure liquids tend to cause bubbles with more mobile surfaces that have a
greater tendency to coalesce. Less pure waters tend to produce smaller, more rigid
bubbles.
For relatively large-diameter bubble columns, interfacial area is usually
approximated by (Roustan et al., 1996):
g
g
bda
1
6(12)
where a is specific surface area (net surface area per reactor volume), db is effective
bubble diameter (diameter of a spherical bubble whose volume is the same as that of the
45
bubble) and g is gas phase holdup (i.e., the gas phase volume divided by the
total reactor volume). For very small gas holdup, interfacial area can be approximated
by
a 6 g
db
(13)
For smaller-diameter columns, the column geometry may influence gas holdup and Akita
and Yoshida (Akita and Yoshida 1974) propose the relation
13.11.05.013.1
1.0
2
35.02
3
1
3
1gaog
L
cLcc GB
dgdgda
(14)
where dc is column diameter, g is gravitational acceleration, L is liquid phase density,
is surface tension, L is liquid phase kinematic viscosity, Bo is Bond number and Ga is
Galileo number. The Akita-Yoshida relation was developed based on analysis of data
from a 2.5 m high rectangular cross section bubble column outfitted with a porous plate
sparger.
Many relations have been proposed for bubble diameter, some of which are
presented in Table 5. These relations must be used with care. First, the relations predict
a single diameter bubble though in reality spargers discharge bubbles with a range of
diameters. Second, small differences in sparger manufacture, fouling of sparger or
corrosion may significantly alter discharge bubble diameter. Finally, relations are
generally derived for bubbles either at the sparger discharge or far enough into the liquid
column that coalescence and other changes are complete and a uniform, steady diameter
is established. Choosing just one of these locations as representative is a simplification.
46
Gas phase holdup is another important design variable because it relates
to the overall transfer area, because it provides an indication of the bubble flow regime in
which the column is operating and because it is relatively easy to measure. As with
relations for bubble diameter, numerous relations have been developed for gas phase
holdup. Gas phase holdup relations that have been proposed in the scientific literature
and are applicable to ozone bubble contactor operation are summarized in Table 6.
Because many of these relations were developed based on empirical measurements care
should be taken to understand the conditions for which the relations were developed
before they are used.
.
Table 5: Summary of Bubble Diameter Relations
Expression Source Sparger Location Notes
db 0.0287 do
1 2 Reo1 3 Reo 2100
0.0071 Reo0.05 10,000 Reo 50,000
Leibson inBenitez (2002)
Any with spacingbetween nozzles > 3 do
Sparger Based on air-water system data. Units ofand do are m.
db
1.7 do
r
1 3
Single bubble regime
1.17(U go ) do
0.8g 0.2 Continuous chain regime
4 mm db 6 mm Jet regime
Heijnen andVan't Riet(1984)
Nozzle Sparger In SI units. Single bubble, continuouschain and jet regime correspond toconditions at low, medium and high gasflow rates, respectively.
db
0.0061 U go do
0.1
d00.08
w
0.38
Coalescing
0.0104 U godo
0.1
d00.07
w
0.0.41
Non - coalescing
Heijnen andVan't Riet(1984)
Porous disc Sparger SI units. The ratio /w is the liquidsurface tension to pure water surfacetension ratio
0.5 mm db 1.0 mm Non -coalescing media
4.0 mm db 6.0 mm Coalescing media
Heijnen andVan't Riet(1984)
Injector/ ejector Sparger
47
48
Expression Source Sparger Location Notes
db 4.15 0.6 g
0.5
v b
L
0.2
9.0104 m
Qg Patm lnPatm
Psp arger
v b 2
L db
0.5g db
1 2
Dudley (1995) Any Column is gas power input, vb is bubble free
rise velocity. Developed for turbinecontactor but widely used for bubblecolumns
db 2.15103 L gU g 0.16 Bín, Duczmal
et al. (2001)Porous plates Column Based on experimental data for large
bubbles in a bubble column. SI units,bubble diameter in mm.
48
49
Table 6: Summary of Gas Phase Holdup Relations
Expression Source Notes
g
1 g 4
dc2 L g
1 8
g dc3
L2
1 12U g
g dc
Akita andYoshida(1973)
According to Deckwer and Schumpe (1993) this relation provides a “reliableconservative estimate” of gas hold-up. For pure liquids and non-electrolytesolutions =0.2 and for salt solutions =0.25.
U g 1 g U L g Vb g 1 g 2.39 Lockett and
Kirkpatrick(1975)
Developed for 5 mm air bubbles in disperse bubbly flow (g < 0.3).
g 0.672 fU g
0.578L
4 g
L 3
0.131 g
L
0.062g
L
0.107 Hikita, Asai etal. (1980)
According to Deckwer and Schumpe (1993), this relation provides slightly betterholdup estimates than the Akita Yoshida relation because variations in gas phaseproperties are accounted for. The value of f is 1 for non-electrolyte solutions andis a function of strength for salt solutions.
g 1.07U g
2
g dc
Kawase andMoo-Young(1987)
Based on theoretical relations developed for Newtonian and non-Newtoniancontinuous phase. The relation shown is for air bubbles rising in water at 20C
U g
g
0.175 Bo1 8 Ga
1 12 Res1 2 g dc
1 2
3.5103 Bo3 4 Res
2 7 1 0.85 g U L U g
Res db U s
L
U s U g
g
U L
1 L
Uchida,Tsuyutani etal. (1989)
Developed for countercurrent bubble flow in a variety of gas-liquid systems. Thisis the only relation identified that directly accounts for the difference betweencountercurrent and other bubble columns.
g U g
0.3 2U g
Langlais,Reckhow etal. (1991)
Assumes bubbles are free-moving and non-coalescent. Based on work byHughmark. 49
50
Expression Source Notes
g C U gx
C x Sparger Column diameter
3.61 0.91 Porous plate 0.15 m
4.25 0.99 Membrane 0.15 m
3.66 0.83 Perforated Plate 0.15 m
3.43 1.03 Porous plate 0.2 m
3.12 1.05 Membrane 0.2 m
2.2 1.06 Porous plate 0.2 m
Bouaifi,Hebrard et al.(2001)
Given the clear dependence of gas holdup on column geometry and sparger type,this relation does not appear general. Units of superficial gas velocity in thisrelation are cm/s.
50
51
II.1.1.2 Interphase Momentum Transfer
In his comprehensive article on bubble behavior, Moore (1959) described bubble
behavior (shape, rise velocity and drag) for bubbles in various liquids and with various
shapes. The parameters governing bubble drag and terminal velocity include liquid
properties (viscosity, density, surface tension, temperature), gas properties (viscosity,
density, surface tension), bubble diameter (which is largely a function of sparger type and
the tendency of bubbles to coalesce) and local acceleration due to gravity. Gas properties
are generally unimportant in determining bubble drag and rise speed. The remaining
parameters can be grouped and described via the dimensionless parameters, listed in
Table 7. Among the parameters making up the dimensionless quantities in Table 7, the
only one over which designers have substantial control is the bubble diameter.
Table 7: Dimensionless Parameters Associated with Bubble Drag and TerminalRise Speed
Name Formula Description
Mortonnumber 32
4
L
o
gM
Morton number is solely a function of liquid properties.Liquid to liquid variations are largely due to differences inviscosity, since surface tension is less variable. LowMorton number fluids are those with Mo < 10-8 and highMorton number fluids are those with Mo > 10-3. Pure waterhas Mo = O(10-10). The precise value depends upon thetemperature and purity of the water. In most casescontaminated water has a higher Morton number (due tothe presence of surface active agents and lower surfacetension) than pure water.
Reynoldsnumber Re
dbVb
L
The ratio of inertial forces to viscous forces. For bubbles,the characteristic length is the effective bubble diameter,defined as the diameter of a sphere whose volume is thesame as that of the bubble. The characteristic velocity isthe bubble terminal rise velocity.
52
Name Formula Description
Webernumber We
db Vb
2
The ratio of hydrodynamic forces to surface tension forces.Where surface tension forces dominate (low Webernumber), bubble shape is that which minimizes surfacetension forces and is spherical. Where hydrodynamicforces dominate, the bubble assumes a shape to minimizedrag.
Eötvösnumber
2b
o
dgE
The ratio of gravitational forces to surface tension forces.
The significance of the bubble diameter and shape in determining bubble drag and
rise velocity is illustrated in Figure 8 (Moore 1959). For small bubble diameters
(generally less than 2 mm for air bubbles in water), bubbles are spherical and rise
rectilinearly. As bubble diameter increases, hydrodynamic forces play an increasing role
in determining bubble shape and bubbles assume ellipsoidal then oblate shapes. As
bubble diameter is further increased, bubble shape fluctuates and trajectories become
zigzag or spiral as bubbles ascend. In this Weber number range, the bubble rise speed
decreases significantly. At what is presumed to be a critical Weber number (Moore
1959), the trailing edge of the bubble becomes unstable in shape and bubbles assume a
spherical cap (mushroom-like) shape. In this regime, the leading (upward) edge of the
bubble has a stable hemispheric shape and a well-defined boundary layer. The rear
surface fluctuates in shape and the local flow field is dominated by turbulent eddies.
53
Figure 8: Bubble Rise Velocity and Discharge Coefficient Schematics (Moore 1959)
Based on the forgoing, care must be used in choosing a drag coefficient relation
consistent with the bubble shape (Weber number regime) encountered in a bubble
contactor. Numerous relations have been proposed and used. The most commonly used
relations describing drag and terminal bubble speed of dispersed bubbles in a liquid
medium are presented in Table 8 and Table 9.
54
Table 8: Summary of Bubble Drag Relations
Relation Source Notes
Various Stokes relation fora sphere risingsteadily at lowReynolds number.
SchillerandNaumann(in Clift,Grace etal. (1978))
For sphericalbubbles rising inthe viscousregime (Re < 800)and widelydispersed in aliquid.
Moore(1959)
Theoreticallybased relations forsingle bubblesrising in stagnantliquids.
C D
24
Re
Stokes regime
24
Re
1 0.1Re0.75 Viscous regime
2
3Eo
1 2117.67 f g
6 7
18.67 f g
2
Distorted particle regime
8
31 g
2Churn turbulent regime
f g 1 g
c
m
Ishii andZuber(1979)
For groups ofbubbles in allflow regimes.Relations aretheoretical andvalidated viacomparison withdata collected bymany researchers.Relations for dragin the distortedparticle and churnturbulent regimesare reported validto gas holdups of0.95. Reynoldsnumber based onbubble diameterand speed of thebubbles relative tothe liquid phase.
C D 24
Re
687.015.0124
e
e
D RR
C
C D
32
Re
Spherical bubbles, high R e
6
183 5M 1 5 W 3 5 Non - spherical bubbles
2.6 Spherical cap bubbles
55
Relation Source Notes
Ihme inClift,Grace etal. (1978).
For rigid sphereswith Re < 104.
C D 4
3
g db
v b2
L
v b L
L db
M o0.149 J 0.857
3.5942.3
3.59294.0441.0
751.0
J
ref
149.0
3
4
Loo ME
Grace (inClift,Grace etal. (1978))
For distorted airbubbles rising inwater. Referenceviscosity is that ofpure water atspecifiedtemperature andpressure and canbe taken as0.0009 kg m-1 s-1.Valid over therange of specified.
36.048.524 573.0
ee
D RR
C
56
Table 9: Summary of Bubble Terminal Speed Relations
Expression Source Notes
L
eBBL
Be
Be
L
Be
BeL
BeBeL
Be
L
GLBe
B
dVR
where
RMg
MRMR
MRRg
RgR
V
,
,
,
25.0
1
25.0
25.0
1,
214.0
1
5.0
,
214.0
1,
28.1
,
52.076.0
,
2
,
10.318.1
10.302.435.1
02.4233.0
29
2
Peebles andGarber(1953)
The variable dB,e is theeffective bubble diameter(the diameter of thesphere that has the samevolume as the bubble) andthe variable M is theMorton number.
VB L
L db
M o0.149 J 0.857
J 0.940.747 2 59.3
3.420.441 59.3
4
3Eo M o
0.149
Clift, Graceet al. (1978)
For single ellipsoidalbubbles rising incontaminated water.Validate for Mo < 10-3, Eo
< 40, Re > 0.1 andaqueous viscosity notsignificantly differentfrom that of pure water.
VB 2 g
L2
1 4
1 g 1.75
Ishii andZuber (1979)
For bubbles in liquids inthe distorted particleregime.
VB 0.574
g
U g
g dc 0.5
2.5 Viswanathanand Rao (inKawase andMoo-Young(1987)
Theoretically-derivedrelation that includesdependence on columndiameter.
VB
210db
1.004
L
0.5 db 1.8mm
20 33.8e4.88db 1.004
L
1.8 db 4mm
Mariñas,Liang et al.(1993)
Empirical relation basedon observations of the riseof single bubbles instagnant liquids. Units ofVB, db and L are cm/s, cmand centipoise,respectively.
VB 2
db
0.5g db
Winkler (inDudley(1995))
57
II.1.1.3 Bubble-Induced Turbulence
Bubbles generate turbulence in their wakes, the practical results of which are
altered drag on other bubbles and changes in mixing. Sato and Sekoguchi (Sato and
Sekoguchi 1975) proposed a turbulence model that accounts for the fact that bubbles in a
shear flow (such as in a turbulent eddy) generate their own turbulence due to form drag.
The authors proposed that instantaneous fluid velocity in a bubble-laden flow can be
expressed as:
V V
V
V (15)
where
V is local instantaneous fluid velocity, V
is fluctuating velocity component
(instantaneous turbulence velocity) inherent in the liquid and independent of the
existence of bubbles and V
is a fluctuating velocity component caused by the motion of
the bubble relative to the surrounding fluid. As with single-phase turbulence modeling,
the velocity expression is introduced into the liquid phase momentum equation and the
resulting equation is averaged. This procedure produces an additional viscosity term in
the momentum equation:
eff L T B,T (16)
where eff is effective viscosity, L is liquid molecular viscosity, T is turbulent viscosity
and T,B is bubble-induced turbulent viscosity. This relation is available as an option in
the commercial CFD code that has been used in numerical simulations in this work.
58
II.1.1.4 Mixing
II.1.1.4.1 Large Scale Hydrodynamics and Mixing
Mixing is critically important in ozone bubble columns. Small scale mixing
(dispersion) renews bubble surfaces with low ozone content liquid and promotes mass
transfer. Dispersion also carries water with high dissolved ozone concentration into
water with low ozone concentration
Mixing in ozone bubble contactors depends on the gas and liquid flow rates in the
contactor and the contactor geometry (Schulz and Bellamy 2000). Properly designed and
mixed operations do not have significant “channeling (short-circuiting)” or temporal
variations in ozone residual at a given location for a given gas and liquid flow rate.
Mixing in industrial ozone facilities is most often assessed based on the coefficient of
variation of time series of ozone residual at the reactor discharge. A coefficient of
variation less than 5% is thought to indicate sufficient mixing and that short-circuiting or
other non-ideal hydrodynamic processes are not significant (Schulz and Bellamy 2000).
When mixing in an ozone bubble contactor is believed to be inadequate, the most
common remedial actions are:
addition of ozonated air or oxygen at a lower ozone concentration and a higher gas
flow rate;
ensuring a dense coverage of diffusers in chambers where gas is introduced;
supplemental mixing with diffused air or water jets;
improvement of intake or discharge hydraulics.
59
Because design data and guidelines for implementing these changes are not available,
experience is the only guide to effective choice and design of appurtenances for
enhancing mixing.
Large scale mixing phenomena determine how well the phases are distributed in a
reactor and the likelihood of short-circuiting or backmixing in the reactor. Bubble
plumes tend to migrate to walls or toward each other, as shown in Figure 9 and Figure 10
(Freire et al., 2002). This effect, sometimes called the Coanda effect, arises because
entrainment of liquid into the bubble plume is constrained on one side.
Figure 9: Migration of a Bubble Plume to a Wall (Freire et al., 2002)
60
Figure 10: Migration of Bubble Plumes toward Each Other (Freire et al., 2002)
In ozone bubble contactors, bubble plume migration may occur, depending on
sparger placement and gas to liquid flow ratio. Depending on the type of feed for the
ozone generator (oxygen or air) and the design gas flow rates, rod and dome shaped
diffusers may be used in full scale fine bubble contactors. Rod shaped diffusers are
usually used when air is ozone generator feed gas and gas flow rates between 0.057 and
0.17 m3/min (2 and 6 ft3/min). Dome shaped diffusers are most often used when oxygen
is the feed gas and gas flow rate is between 0.014 m3/min and 0.17 m3/min. A guideline
for sparger spacing 4 ft2 or less per diffuser (Rakness 2005).
Numerous studies have been made of large-scale mixing in bubble columns with
non-flowing liquid phase (Grevet et al., 1982; Anderson and Rice 1989; Drahos et al.,
1992; Burns and Rice 1997; Lapin et al., 2002) but only one (published in multiple parts)
was identified that described or quantified large scale mixing in countercurrent flow
61
columns (Anderson and Rice 1989; Burns and Rice 1997). In columns with non-flowing
liquid phase, bubble plumes entrain liquid as they rise, establishing regions of circulating
flow outside the bubble plume. The size and arrangement of these circulations is
dependent on the gas flow rate and the reactor geometry. Shallow bubble beds (height /
diameter 2) with non-flowing liquid phase establish a single circulation cell outside the
bubble plume. Bubble beds with larger height to diameter ratios establish multiple cells
(Drahos et al., 1992).
In countercurrent flow in cylindrical reactors, liquid flow tends to be upward in
the “core” of the bubble plume, and downward outside the bubble plume near the wall
(Burns and Rice 1997). The presence of a strong liquid down flow outside the bubble
plume reduces the amount of recirculation in the liquid phase. At high gas to liquid flow
ratios (but below churn turbulent flow) the bubble plume tends to grow in diameter more
slowly as it rises compared plumes at lower gas to liquid flow ratios.
For tall cylindrical bubble columns, minor misalignments of the centerline from
vertical can result in drastic differences in liquid flow (Rice and Littlefield 1987). In the
cited study, the authors filled a cylindrical bubble column with a solution of hydrochloric
acid and a pH indicator, sparged air into the solution until steady state hydraulics were
achieved, then pumped a strong solution of sodium hydroxide into bottom of the reactor.
As the sodium hydroxide progressed upward in the reactor, the pH indicator changed
color. Near the sparger the reactor behaved like a continuously stirred tank reactor
(CSTR) and the progress of the line of neutralization could not be followed. Above the
entrance region, the line of neutralization between the acidic and basic regions tended to
be distinct and to rise steadily. The progress of the line of neutralization was recorded on
62
video tape. The rate of rise of the line of neutralization was computed from the video
images and the liquid phase dispersion was calculated via fitting a one-dimensional axial
dispersion model to observed rates. Two findings drawn from that study are of
importance to the current study. First, minor vertical misalignments (less than 0.5°) of
the column from true vertical resulted in major differences in dispersion. Second, an
“entrance region” was determined to exist near the sparger. This entrance region behaved
as a plug flow reactor. Regression was used to determine model parameters (dispersion
and height of the entrance region) that best fit experimental data. Unfortunately the
authors did not report the dependence of the height of the entrance region on gas flow
rate.
II.1.1.4.2 Small Scale Hydrodynamics and Mixing
Bubbles give rise to liquid-phase hydrodynamic dispersion in bubble columns and
dispersion, in turn, influences mass transfer rates. To date most analyses have
approximated liquid dispersion in a bubble column via a single dispersion number
(inverse of Peclet number) though dispersion likely varies axially in bubble columns. For
example, in a study of cocurrent air-water flow in bubble columns, Deckwer, Burckhaart
et al. (1974) found that dispersion was lower in the vicinity of the sparger compared with
dispersion in the rest of the column. In a study of a bubble column with no net liquid
flow, other authors determined the region near the sparger behaved as a CSTR (Rice and
Littlefield 1987).
Lehrer (1984) identifies the following parameters as influencing dispersion:
Gas and liquid flow rates;
63
column dimensions;
configuration of fluid injection; and
properties of fluids.
Based on these observations, the author proposed a relation for axial dispersion of the
form:
EL EBB EK i
i1
N
QbU g (17)
where EL is the axial dispersion, EB is the contribution due to bubble form drag, B is a
hindered motion factor which accounts for interactions between bubbles, EK is the
contribution due to fluid injection through sparger holes, N is the number of sparger
holes, Qg is gas volumetric flow rate and Ug is gas superficial velocity. This relation has
limited applicability, given that for high gas flow rates the turbulent dispersion can
decrease or even become negative.
A number of relations for liquid phase dispersion commonly cited in the literature
are provided in Table 10. The conditions under which data supporting these relations
were taken are provided in the notes. These conditions should be given careful attention
given the importance of sparger type and reactor geometry in dispersion.
64
Table 10: Axial Dispersion Relations
Relation Source Notes
EL 2.7 d c1.4 U g
0.3 Deckwer,Burckhart etal. (1974)
Developed for cocurrentflow of air in water,molasses and salt solutionsin two cylindrical bubblecolumns of 15 and 20 cmdiameter and 4.4 and 7.23 mwater column heights. Unitsof column diameter, dc, andsuperficial gas velocity, Ug,and liquid phase dispersion,EL, are cm, cm/s and cm2/s,respectively.
315.190.0 sggcL UUHdE Field andDavidson(1980)
Developed for cocurrentgas-liquid flow with Ug >>UL. In this equation Us isslip velocity and units arem2/s, m, m, m/s and m/s forEL, dc, H, Ug and Us,respectively.
EL 1.3134g 0.2 N 0.2 Qg0.6 tanh
0.168g 0.2 dc
N 0.3 Qg0.4
1 2
QU g
Lehrer(1984)
Theoretical relationdeveloped based on energyimparted to the liquid streamby gas injection, bubble dragand friction on columnwalls.
67
35
21
1 7.900185.088.4
b
L
L
g
edU
U
Hp
Kim,Tomiak etal. (2002a)
Developed based onexperimental observation inright circular cylindricalbubble columns. Units ofcolumn height, H, are m.Units of other variables mustbe dimensionally consistent.
6.03231
1.0
123511
3.1
areg
e
c
eGFR
R
d
HP
Moustiri,Hebrard etal. (2001)
Developed for cocurrentgas-liquid flow incylindrical columns. Theauthors found a pronouncedeffect of column diameter,fluid superficial velocitiesand bubble regime ondispersion.
65
II.1.1.5 Interphase Ozone Mass Transfer
The first step in the dissolution of an ozone molecule is transport of the molecule
from the bulk gas phase (interior of a bubble) to the gas-liquid interface. As the ozone
molecule approaches the interface, it encounters resistance to its transport. This
resistance is a result of forces between gas and liquid molecules at the bubble surface and
additional forces related to the accumulation of surface active agents at the bubble
surface. These surface active agents accumulate as bubbles rise, explaining, in part, the
dependence of mass transfer rate on bubble age or reactor height. Surface active agents
are thought to produce interfacial resistance through formation of an energy barrier,
formation of a physical “sieve” that blocks some gas molecules or by influencing small
length scale hydrodynamics near the bubble surface (Goodridge and Robb 1965;
Vasconcelos et al., 2002; Alves et al., 2005).
At the bubble length scale, features that influence mass transfer are the shape of
the bubble, fluid motion on the length scale of the bubble diameter and proximity of other
bubbles. As illustrated, to accurately predict mass transfer, one must account for bubble
surface area (shape and effective diameter), gas phase hold-up, gas phase distribution,
liquid phase dispersion and circulation and chemical properties at the bubble surface.
Along with mass transfer, there is momentum transfer between the gas and liquid
phases. Momentum transfer results in enhanced turbulence and may lead to an increase
in dispersion and mixing, though not necessarily. In bubble columns and other
multiphase mass transfer operations, efficient mass transfer is facilitated by contacting
the phases in such a way that the difference in concentration of the material that is
66
transferred is a maximum. So, countercurrent bubble columns (in which the liquid flows
downward and the gas bubbles upward) are preferred over cocurrent configurations.
Since the early 20th century, numerous researchers have sought to identify the
features that govern mass transfer between bubbles and liquids and have proposed
relations to predict the rate of transfer. The features that may govern mass transfer have
been identified as:
The manner in which bubbles are introduced into the contactor;
Liquid physical properties (viscosity, surface tension and dissolved ozone diffusivity;
The superficial gas flow rate;
The rate of dissolved ozone consumption in liquid phase reactions;
The presence of surface-active contaminants;
The contactor geometry (especially the ratio of the diffuser area to the contactor cross
sectional area and diffuser height); and
Bubble age.
Table 11 summarizes dimensionless parameters for characterizing bubble column mass
transfer.
67
Table 11: Dimensionless Parameters Relevant to Bubble Column Mass Transfer
Dimensionless parameter Formula
Bond numberBo
g dc3 L
Froude numberFr
U L2
g d c
Galileo numberGa
g dc3
L2
Peclet number
i
Bg
eD
dUP
Reynolds numberRe
U g db
L
Schmidt numberS c
L
D i
Sherwood numberS h
kL dB
D i
In development of early models of the dissolution of gases, it was hypothesized
that there are thin layers of stagnant fluid on both sides of the gas-liquid interface, as
illustrated in Figure 11. In order for a gas molecule to diffuse from the bulk gas phase to
the bulk liquid phase, it must first overcome the gas film resistance, the resistance of the
surface layer and the liquid film resistance. The flow in the gas and liquid films is
assumed laminar and flow in the bulk phases is usually assumed to be turbulent.
68
Bulk gas phase
Gas film
Liquid film
Bulk liquid phase
Gas film resistance
Surface layer resistance
Liquid film resistanceL
Lk
R1
s
sk
R1
G
Gk
R1
Figure 11: Schematic Diagram of the Two-Film Mass Transfer Model
Surface resistance depends upon the composition of the gas and liquid phases and
the presence of surface active agents that accumulate at the gas-liquid interface. Surface
active agents are hypothesized to offer resistance to gas diffusion via (Goodridge and
Robb 1965):
development of an energy barrier that impedes the progress of low-energy gas
molecules;
a sieving effect caused by the collision of gas molecules with surface agent agent
molecules assembled at the gas-liquid interface;
alteration of the hydrodynamics and size of the gas and liquid films adjacent to the
gas-liquid interface.
Surface active agents alter mass transfer rates indirectly by influencing the nature of the
bubble surface and consequently the bubble size, shape and tendency to break up or
69
coalesce with other bubbles. The presence of trace concentrations of surface active
agents tends to change the mobility of bubbles surfaces (Clift et al., 1978; Alves et al.,
2005), the effective bubble diameter and holdup observed at a given liquid and gas flow
rate (Anderson and Quinn 1970). In studies of carbon dioxide sparged into distilled
water, de-ionized water and tap water, bubble coalescence was significantly lower in tap
water than in either de-ionized water or distilled water (Anderson and Quinn 1970). The
authors attributed this finding to the presence in tap water of substances that decrease the
mobility of bubbles and the possible presence in trace concentrations of coalescence-
promoting substances (possibly from resins in deionizing filters) in distilled and
deionized waters. For the ozone-water system, the Henry’s law constant varies with pH
and ionic strength as well as temperature (Bín 1995). The impact of surface active agents
on mass transfer is profound – the rate of dissolution of gases into waters with very low
ionic concentration is more than twice that into tap water (Alves et al., 2005).
Surface active agents (Vasconcelos et al., 2002; Alves et al., 2005) and
microorganisms (Blanchard 1970; Wozniak et al., 1976) accumulate on bubble surfaces
as bubbles rise through contaminated liquids. This accumulation explains the observed
dependence of mass transfer on bubble age. In studies of bubble rise velocity and mass
transfer rates of single bubbles, the rise velocity and mass transfer rate were both found to
decrease as a function of time as surface active materials accumulated on the bubble
surface. Liquid side mass transfer coefficient was found to lie between the value
predicted by penetration theory (which assumes a completely mobile bubble surface and
is described below)
70
b
sL
d
Duk 13.1mobile (18)
and that predicted for a bubble with a rigid surface
6132rigid 6.0 Dd
uk
B
sL (19)
In equations 17 and 18, us is slip velocity (relative velocity between the bubble and
liquid), D is molecular diffusivity, dB is bubble diameter and is dynamic viscosity of the
liquid phase. The phenomenon of bacterial accumulation on bubble surfaces does not
impact mass transfer, but does influence the transport of microorganisms and the
uniformity of their contact with disinfectant.
Mass transfer models proposed after the two-film model recognized that the gas
and liquid film are not likely to be stagnant. Rather, fresh liquid and gas are continuously
exchanged between the films and bulk phases. The hydrodynamics related to the
transport of ozone from bubbles to the bulk liquid phase are illustrated in Figure 12. At
the bubble scale, gas phase circulation within the bubble influences the distribution of
ozone in the gas phase, the shape of the bubble and the rate at which ozone is transported
from the bulk gas phase to the gas-liquid interface. In the liquid phase, small scale
turbulence present in the bubble wakes and generated via hydrodynamic dispersion
transport liquid from the bulk phase to the bubble surface. Large scale fluid structures
(with length scale equal to the bubble column diameter) advect dissolved gases away
from the bubble plume and, in the case of uneven distribution of phases, into the liquid
phase.
71
Low ozoneconcentration
downwardflowing liquid
Ozone-rich liquid inthe bubble plume
Gas phasecirculation
Liquidrenewal atthe bubble
surface
Figure 12: The Hydrodynamics of the Transport of Ozone from Gas Phase to theBulk Liquid Phase
In the first mass transfer model proposed to account for realistic exchange of
liquid between the bulk phase and film (called penetration theory), it was hypothesized
that parcels of “fresh” liquid from the bulk phase are in contact with the interface for a
characteristic time (Higbie 1935). During the contact time between the fluid parcel and
interface, dissolved gases “penetrate” into the fluid parcel. Fluid parcels having longer
contact times with the bubble surface experience greater depth of penetration of the
dissolved gas into the fluid parcel. Dissolved gas penetrates into the fluid parcel fastest
during initial contact of the parcel with the bubble surface when the dissolved gas
concentration in the fluid parcel is low. After long contact times the dissolved gas
concentration in the fluid parcel increases and the flux of dissolved gas into the fluid
parcel decreases. Assuming negligible gas phase resistance to mass transfer, penetration
72
theory predicts the absorption rate for fluid parcels with a contact time of with the gas-
liquid interface is given by
D
CC 0* (20)
where C* is gas phase concentration divided by Henry’s law constant, C0 is the initial
dissolved gas concentration in the fluid parcel and D is the diffusivity of the dissolved
gas in the liquid. Assuming the contact time between a fluid parcel and the bubble
surface is equal to the bubble diameter divided by the slip velocity, Higbie’s penetration
theory predicts the liquid mass transfer coefficient is given in equation 18 (repeated
below)
b
sL
d
Duk 13.1 (18)
Since the penetration theory was proposed, researchers have proposed alternative
mass transfer models in which the contact time between fluid parcels and the gas-liquid
interface is not uniform. Danckwerts (1951) suggested that fluid parcels are exchanged
randomly at the gas-liquid interface and that the overall mass transfer coefficient at a
given time is the integrated mass transfer to all fluid parcels (with a distribution of
contact times with the gas-liquid interface) at the interface. This model, in which parcels
are renewed at the interface with some distribution of parcel contact times, is called the
“surface renewal” model. These assumptions give rise to the mass transfer rate
sDkL (21)
where s is the random replacement rate for fluid particles at the interface (units of T-1).
73
Although it may better reflect interface processes, relation 10 is used for
predicting mass transfer rate less often than equation 7, perhaps because of the difficulty
in estimating the replacement rate. Since the introduction of the surface renewal model,
other investigators have developed mass transfer models using various distributions of
parcel residence times at the interface. For example, a mass transfer model assuming the
distribution of parcel residence times at the interface was given by the gamma
distribution provided improvements in mass transfer prediction in turbulent pipe flow
over predictions based on Danckwerts’ model (Harriott 1962). Although the replacement
rate for parcels is likely related to the distribution of eddy sizes in turbulent flow, no
studies were found that related mass transfer coefficient to distribution of turbulent
kinetic energy.
The most commonly used relations for mass transfer are presented in Table 12.
The relations are presented as they were presented in original publications except where
the original nomenclature conflicts with that used in this dissertation. The basis
(theoretical, empirical and semi-empirical) for the relation and notes on the data on which
the relations were developed are also presented. Among the relations in Table 12, the
Hughmark relations (Hughmark 1967a; Hughmark 1967b) are most widely used and
basic mass transfer text books present them as the de facto standard for bubble contactor
design (Rakness et al., 1988; Benitez 2002). Although the Hughmark relations are
convenient to use and have long records of accomplishment, care should be taken in
choosing and using them – Hughmark’s original papers presented several alternate
relations appropriate for different flow regimes. The correct formula should be chosen
and justification should be provided for that choice.
74
Calderbank and Moo-Young (1961) determined that the two most important
parameters in determining interphase mass transfer between dispersed bubbles and a
continuous liquid are diffusivity of the gas diffusing into the liquid and the size and flow
regime of the bubble. In general, mass transfer rates from larger bubbles is greater than
that from small bubbles, presumably because in large bubbles form drag predominates,
while friction drag predominates for small bubbles. The hydrodynamics associated with
friction drag present a barrier to penetration of dissolved gas into a continuous liquid,
while turbulent wakes behind large bubbles disperse dissolved gases away from bubbles
and bring low-concentration fluid in contact with the bubbles. Large diameter bubbles
were considered those with a diameter greater than 2.5 mm. Motarjemi and Jameson
(1978) validated the Calderbank and Moo-Young expressions for large and very small
bubbles, but found that in the transition region between small and large bubbles, the mass
transfer was significantly higher than that predicted by Calderbank and Moo-Young.
Their finding led them to propose an optimal bubble size of 1 mm for oxygen transfer in
air-tap water systems.
The debate over small and large bubble behavior should also consider the
presence of surface-active contaminants in the water and their effect on bubble size,
shape and behavior. Anderson and Quinn (1970) found a marked difference between gas
phase holdup and bubble shape between experiments with air bubbled in distilled water
and air bubbled in tap water. When bubbled in distilled water, air bubbles had a greater
tendency to coalesce and form spherical cap bubbles. In concluding, the authors caution
that trace amounts of contaminants may drastically change bubble column mass and
momentum transfer behavior and that, in conducting tracer experiments, care should be
75
taken in choosing a tracer that does not have surface-active properties. Dudley (1995)
states that surfactants reduce surface tension, resulting in greater specific surface area.
However, surfactants also alter gas diffusivity in the aqueous phase and make bubble
surfaces more rigid. The net result of the presence of surfactants is a net reduction in kLa
in contaminated waters compared with transfer in pure water. Deckwer, Burckhart, et al.
(1974), like Dudley, noted that while specific surface area increases as surfactants are
introduced into the liquid phase, mass transfer coefficient, kL, reduces. This is attributed
to the formation of an electric double layer at the gas-liquid interface that impedes the
diffusion of dissolved gas into the aqueous phase. Prior researchers have suggested
mechanisms other than formation of an electric double layer to explain the way in which
surfactants impede mass transfer (Goodridge and Robb 1965). These mechanisms
including a “sieving effect” (physical entrapment of gas molecules by a thin surfactant
film) or hydrodynamic effects such as change in mass transfer boundary layer thickness
or local turbulence scale at the gas-liquid interface. In a recent study, it was suggested
that the major influence surfactant have on mass transfer relates to the impact of surface
active agents on bubble size and shape (Sardeing et al., 2006).
Dudley (1995) evaluated a number of mass transfer coefficient expressions
developed using a theoretical basis or data from co-current and non-flowing liquid bubble
columns (Calderbank and Moo-Young 1961; Motarjemi and Jameson 1978; Khudenko
and Shpirt 1986; Öztürk et al., 1987; Kawase and Moo-Young 1992) against
experimental mass transfer data collected in a 0.2 m diameter bubble column with a
height of 4 m and non-flowing liquid phase. Two diffusers of differing diameter and
unspecified type injected air into the columns. Liquid height, gas flow rate and liquid
76
composition were varied. The relation providing the best correlation with the
experimental data was that of Kawase and Moo-Young (1992). Dudley recommends the
Kawase relation for general use because of its good correlation with data and its
theoretical basis.
Heijnen and Van’t Riet (1984) suggest the use of the Higbie relation for bubbles
of diameters larger than 2 mm in diameter. This suggestion is made based on analysis of
mass transfer data from many sources but is questionable given the tendency of
surfactants to make bubbles more rigid (more like small bubbles) and the conclusion of
Calderbank and Moo-Young (1961) that the transition between small and large bubble
behavior is for bubbles whose diameter is between 1 and 2.5 mm. The range of mass
transfer coefficients expected in typical bubble columns for bubbles of average diameter
greater than 2 mm is 2 10-4 m/s < kL < 3 10-4 m/s. For bubbles of average diameter
less than 0.8 mm the transfer coefficient is insensitive to bubble diameter and
approximately 1 10-4 m/s.
7777
Table 12: Summary of Mass Transfer Relations for Dispersed Bubbles in Continuous Liquids
Author Relation Basis2 Description
Higbie (inMotarjemiand Jameson(1978))
kL 2
D i
te
2
D i U s
Lc
2
ReS c
Pe
T Developed based on penetration theory. The variable te is the time totraverse one bubble diameter and corresponds roughly to the contacttime between liquid fluid parcels and bubble surface. This relationwas proposed based on an assumption that form drag predominatesand bubble surface is mobile. The relation is most appropriatelyused for large bubbles.
Froessling (inMotarjemiand Jameson(1978))
S h 0.6 Re1 2 S c
1 3 T Developed from potential flow theory for small spherical rigidbubbles. This relation was proposed based on the assumption thatfriction drag predominates and mass transfer takes place through alaminar boundary surrounding the bubble. This relation is mostappropriately used for small bubbles.
Calderbankand Moo-Young (1961)
kL
0.31
L
gD i
S c
1 3
Bubble swarms, dB 2.5 mm
0.42
L
g 2Di
2
S c
1 6
Bubble swarms, dB 2.5 mm
E Correlations developed based on historical data and data collectedfor a variety of gas-liquid systems and with a variety of diffusers.The units of kL depend on the choice of units for g and Di. Figuresincluded in the paper indicate that small bubbles might be more-appropriately designated as those 1 mm or smaller in diameter.
Hughmark(1967b)
S h
2 0.6Re1 2S c
1 3 1 Re 450; S c 250
2 0.5Re1 2S c
0.42 1 Re 17; S c 250
2 0.4Re1 2S c
0.42 17 Re 450; S c 250
2 0.27 Re0.62S c
1 3 450 Re 104; S c 250
2 0.175Re0.62S c
0.42 450 Re 104; S c 250
E Developed based on mass transfer data from single, rigid spherestaken for a variety of species dissolving into a variety of liquids.
2 Designations are: “T” for theoretical, “E” for empirical and “SE” for semi-empirical (based on calibrated models developed from the Buckingham pi
theorem).
7878
Author Relation Basis2 Description
Hughmark(1967a)
S h 2 a Re0.484S c
0.339 dB g1 3
D i2 3
0.072
b
a=0.061, b=1.61 for individual gas bubbles
a=0.0187, b=1.61 for bubbles in swarms
E Developed based on bubble column data from numerous sources andwith a variety of gas-liquid systems (CO2-water, Air-Water, Air-glycerol, air-aqueous solutions). Sherwood number is based onbubble diameter and dissolved gaseous species diffusivity.
7979
Author Relation Basis2 Description
Lochiel andCalderbank(1964)
For rigid bubbles (fixed shape):
Sh
0.99Pe1 3 Re 1; spherical bubble
0.84 Re1 2Sc
1 3 Re 1; spherical bubble
Sh,sphereE2 2
3(1 k)
1 2
All Re , oblate spheroids
For bubbles with mobile interfaces,
Sh
0.65L
L G
1 2
Pe1 2 Re 1; spherical bubble
1.13 12.96
Re1 2
1 2
Pe1 2 Re 1; spherical bubble
Sh,sphere
2
31 k
1 2
All Re , oblate spheroids
Where
2E1 3 E 2 1
E E 2 1 ln E E 2 1 E1 6
k eE 2 Esin 1 e
eEsin 1 e
e 11
E 2
T Theoretical relations developed for high Peclet and Schmidt numbercases. Relationships were derived for single bubbles of knownshape. Relationships were also developed for spherical cap shapedbubbles, but these are not presented here because spherical capbubbles are unlikely to be encountered in ozone bubble contactors.
8080
Author Relation Basis2 Description
Deckwer,Burckhart etal. (1974)
kL a b0 U gb1
where b1=0.0086 and b1 = 0.884 correspond to a 20 cmdiameter bubble column of total height 7.23 m outfittedwith 56 injector nozzles and b1=0.0274 and b1 = 0.8correspond to a 15 cm diameter bubble column of totalheight 4.4 m outfitted with 56 porous plate injector.
E Based on measurement of interfacial area and mass transfer incocurrent flow bubble columns of varying diameter and injectortype. Liquids in the bubble column were water, assorted saltsolutions and molasses. Oxygen transfer was observed and it isassumed that air was the dispersed phase gas.
Akita andYoshida(1974)
Sh 0.5 Sc1 2 Ga
1 2 Bo3 8 E Mass transfer and specific surface area data were collected in three
bubble columns. The columns had square cross sections and were2.5 m tall. The cylinder side dimensions for the three columns were7.7 cm, 15 cm, and 30 cm. Single orifice spargers were used for allthree columns and porous plate and perforated plate spargers wereused in the 15 cm column. Oxygen and air were employed as thedispersed gas phase fluid. Numerous liquids were used as thecontinuous fluid, including water, glycol solutions, glycerolsolutions, methanol and sodium sulfite solution.
Jackson andShen (1978)
kL
a 20
2.37 U g1.07H0.45 Based on previous data
2.28 U g1.14 H0.55 Based on 1.8m tank data
0.53 U g1.15 Data from all experiments
E Based on air bubbled into deoxygenated water or mixed liquor.Three tanks (76 mm, 1.8 m and 3.6 m diameters) were used. Asingle nozzle injected gas into the 76 mm column. Four nippleswere used as injection sites in the 1.8m diameter tank. Fifty-nineinjection sites (holes drilled in pipe wall) were used in the 7.6 mdiameter tank. H is liquid depth with no gas holdup and (kLa)20 ismass transfer coefficient at 20ºC in units of hr-1.
8181
Author Relation Basis2 Description
Khudenkoand Shpirt(1986)
kL a 0.041 h
db
0.67f
W
0.18U g
H
SE This relation was developed via dimensional analysis and calibrationwith experiments performed in rectangular tanks of three sizes.Liquid-gas systems were deoxygenated tap water and air. Twodiffusers and several diffuser spacings were employed. The transferparameter kLa has units of hr-1. Variables 1 and 2 are correctionsfor the presence of contaminants and the deviation of temperaturefrom 20ºC, respectively. H and h are the column height and aeratorsubmergence depth. W is the width of the aeration tank.
Roustan,Duguet et al.(1987)
kL a 0.0139U g0.82 E This expression was developed based on fitting an assumed power-
law relation between transfer rate and superficial gas velocity toexperimental data collected in a full-scale ozone contactor. The gas-liquid system observed was ozonated air – filtered water. Columnheight was 4.3 m and porous disc diffusers were used to introduceozonated air into the contactor. Units of kLa corresponding to thisrelation are min-1 and Ug is superficial gas velocity (gas volumetricflow rate divided by reactor cross sectional area) in units of m/hr.
Öztürk,Schumpe etal. (1987)
S h 0.62 S c0.5 Bo
0.33 Ga0.29 Fr
0.68 g
L
0.04 E Developed based on measurements in a cylindrical bubble column(diameter of 0.095 m, height of 0.85 m). A single gas distributorwas used with 50 different gas-liquid systems. Carrying gases wereair, nitrogen, carbon dioxide helium and hydrogen. Liquid phasewas 17 pure organic liquids and 22 mixtures of organic liquids withwater.
Uchida,Tsuyutani etal. (1989)
kL a dc2
Di
0.17 S c0.5 BO
0.62 G A0.31 g
1.1
0.17 D i0.5 dc
0.17 L0.12 g 0.93 L
0.62 0.62 g1.1
E Developed based on experimental measurement of oxygen transferinto deoxygenated liquids including distilled water, glycerolsolutions, butanol solutions and aqueous solutions containing asurface active agent. A right circular cylindrical bubble column wasoperated in countercurrent mode with variable superficial gasvelocities. A porous ball glass filter gas distributor and single nozzlewere used for air injection. Units for kLa are sec-1.
8282
Author Relation Basis2 Description
Kawase andMoo-Young(1992)
kL
0.28g D i
2
L
1 3
Newtonian liquid, dB 2.5 mm
0.47g 2 D i
3
1 6
Newtonian liquid, dB > 2.5 mm
T Developed for rigid, small bubbles behaving as solid spheres andrising in Newtonian fluids. Trace amounts of contaminants maymake small bubbles behave as rigid spheres. Relations developed inthis study are similar to the empirical relations of (Calderbank andMoo-Young 1961) and provide theoretical backing for their use.The equations are dimensionally consistent. Relations are alsodeveloped for two-phase mass transfer in non-Newtonian liquids.
LeSauze,LaPlanche etal. (1993)
kL a U g
, 0.06, 0.5 Re 2100
0.06, 0.7 Re 2100
E Developed based on measurements in a pilot ozone contactor withcircular cross section, 4.3 m height, 0.15 m diameter, a porous platediffuser and undergoing countercurrent flow. Units of superficialgas velocity and kLa are m/s and s-1, respectively.
Roustan,Wang et al.(1996)
kL a 0.105U g
0.564 Re 680
0.055U g0.564 1912 Re 2986
E Developed for countercurrent flow of ozonated air bubbles in a pilotozone contactor (0.15 m diameter, 2.5m height) outfitted with aceramic porous distributor. The predominant bubble shape waselliptical. Units of kLa and Ug (superficial gas velocity) are min-1 andm/hr, respectively.
83
II.1.2 Ozone Demand, Decomposition and Properties
When ozone is exposed to filtered water, there is a fast decrease in ozone
concentration followed by a decrease that can be modeled with first order kinetics
(Langlais et al., 1991; von Gunten 2003a). The stability of dissolved ozone is affected by
pH, ultraviolet light, ozone concentration and the concentration of ozone scavengers.
Because ozone decomposition kinetics are complex and because of the many factors that
influence the chemistry of ozone decomposition, rate constants are typically determined
experimentally for waters in batch experiments. Ozone decomposition is thought to be a
bimolecular process involving ozone and hydroxyl radicals and with a rate expression
given by:
d[O3]
d t k [O3][OH -] (22)
However, rate data are most often reported via a pseudo-first-order rate constant, kO3,
where
kO3
k
[OH -](23)
Researchers (LeSauze et al., 1993) have developed expressions of the form
log kO3 a b pH +c log[TOC] d log[TA] (24)
where a, b, c, and d are experimentally-determined constants and [TOC] and [TA] are
concentrations of total organic carbon and total alkalinity.
84
Examples of rate constants and the conditions under which they were determined
are found in Table 13. Depending upon the water quality, ozone half-life in water can
range from the order of seconds to hours (von Gunten 2003a). Ozone decomposition is a
strong function of temperature, with ozone decomposing much slower at low
temperatures (below 10°C). Ozone plants operating in regions that undergo large
seasonal variations in raw water temperature must install ozone-quenching units
downstream of bubble contactors because low temperatures result in very high ozone
residuals downstream of ozone contactors presenting potential corrosion or human health
concerns. Conversely, high raw water temperatures necessitate application of high ozone
doses to maintain desired ozone concentration in contactors.
Table 13: Ozone Decomposition Rate Constants
kO3Source Conditions
0.011 s-1 Tang, Adu-Sarkodie etal. (2005)
Filter effluent from the ACWD treatmentplant, Fremont, CA, at 20°C, pH 7.3, 3.5mg/L TOC, total alkalinity 82 mg/L asCaCO3.
0.0025 s-1 Kim, Rennecker et al.(2002b)
Treated Ohio River water at 298 K (dataare given as activation energy andfrequency factor)
0.0017 - 0.018 s-1 Roustan, Wang et al.(1996)
Tap water (source not given) with 12ºC <T <19ºC, 7.5 < pH < 8.1, 75 < [TA] < 150mg/L and 0.8 < [TOC] < 6.0 mg/L
0.0045 – 0.019 s-1 Mariñas, Liang et al.(1993)
Filtered treated water with 12ºC < T <25ºCand 8.3 < pH < 8.4
85
For mass transfer calculations, the most important ozone properties are ozone
Henry’s law constant and liquid phase molecular diffusivity. Ozone is considerably more
soluble in water than oxygen or nitrogen. Ozone’s Henry’s law constant increases with
temperature and pH and can be calculated using the expression:
KH 3.87107 [OH -]0.035 exp2428
T
(25)
where H is ozone Henry’s law constant in atm/L/mol and T is temperature in K (Langlais
et al., 1991). Molecular diffusivity also varies with temperature and can be calculated by
DO3 1.10106 exp
1896
T
(26)
where DO3has units of m2/s and T has units of K (Johnson and Davis 1996).
II.1.3 Disinfection Byproduct Formation
Von Gunten (2003b) divides ozone’s potential by-products into those formed in
the absence of bromide and those formed in the presence of bromide. Among those
formed in the absence of bromide, the predominant by-products are from the oxidation of
natural organic matter (NOM) by ozone. The resulting products can be aldehydes,
ketones, keto aldehydes, carboxylic acids, keto acids, hydroxy acids, alcohols and esters.
The main concern with these products is that they are readily biodegradable and may
promote biofouling in distribution systems. In the presence of bromide, disinfection
byproducts may include bromate, a regulated potential human carcinogen, and
86
brominated compounds including trihalomethanes (THMs, presumed human carcinogens)
and halogenated acetic acids (HAAs, also regulated and among which are presumed
human carcinogens) (Westerhoff et al., 1998). The common ozone DBPs are illustrated
in Figure 13.
Figure 13: Significant Ozone Disinfection Byproducts (Song et al., 1997; UnitedStates Environmental Protection Agency 1999; von Gunten 2003b)
The most problematic ozone byproducts, are those formed in the presence of
bromine, and particularly bromate. Bromide occurs naturally in water due to salt-water
intrusion and special geological formations or due to human activity including coal
87
mining, potassium mining and chemical production (von Gunten 2003b).
When ozone oxidizes NOM in the presence of bromide, a number of bromo-
organic byproducts may be formed. Concentrations of those compounds are usually far
below levels of human health concern. Bromate, however, has been classified as a
potential human carcinogen and the U.S. EPA has established a maximum contaminant
level (MCL) of 10 g/L for bromate in finished drinking water. In general, VonGunten
states that bromate production is not a concern for waters with a bromide concentration
less than 20g/L. For waters with bromide in the 40 – 100 g/L range, bromate
production may exceed acceptable levels and minimization strategies may have to be
employed. Above bromide concentrations of 100 g/L, bromate production during
ozonation will be very high.
Bromate forms in the presence of ozone via multiple pathways involving
dissolved ozone and hydroxyl radicals. Numerous authors (e.g., von Gunten (2003b))
indicate that both ozone and hydroxyl radicals must be included in a credible bromate
formation model and that “a simulation within a factor of two relative to the measured
bromate concentration has to be considered satisfactory” in modeling. An illustration of
the most significant pathways for bromate formation is shown in Figure 14. Note that the
mechanisms shown do not include NOM. In general, NOM tends to decrease bromate
formation by consuming bromide and ozone.
Roustan, Duguet et al. (1996) suggest that an approximate simplified bromate
88
formation model is:
k1
O3 Br - BrO - O2 k1 160M -1s-1 at 20C
HOBr BrO - H pKa 9.0 (or 8.8) at 20C
k2
2 O3 BrO - 2O2 BrO3- k2 100M -1s -1 at 20C
Figure 14: Bromate Formation Pathways (Song et al., 1997)
Applying the Roustan bromate formation mechanism in ideal plug flow reactor (PFR)
and continuously stirred tank reactor (CSTR) models, the authors determined that at
89
similar operating conditions the two reactor types discharged similar bromate ion
concentrations, but that to achieve a desired level of infection a CSTR requires a greater
Ct than a PFR. The authors caution strongly that the proposed bromate formation model
does not take into account hydroxyl radical formation and may yield misleading results.
Experimental investigations into the complex mechanism responsible for bromate
formation led Song, Donohoe et al. (1996) to the following conclusions:
increasing bromide, ozone dose, pH or inorganic carbon concentration increases
bromate formation;
Increasing dissolved organic carbon (DOC) or ammonia nitrogen tends to decrease
bromate formation;
Increasing contact time tends to increase bromate formation; and
increasing temperature tends to promote bromate formation.
The order of importance of the parameters in bromate formation is shown in Table 14.
Strategies for minimizing bromate formation in ozone contactors include
ammonia addition, pH reduction, hydroxyl radical scavenging or reduction of
hypobromous acid. The most practical of these solutions are ammonia addition and pH
depression (Pinkernell and Von Gunten 2001). In a study of concurrent inactivation and
bromate minimization, Driedger, Staub et al. (2001) demonstrated the feasibility of
bromate control while achieving target inactivation rates using both pH depression and
90
ammonia addition.
Table 14: Factors Influencing Bromate Formation
Order of importance for parameters that tend to increase bromate formation:
pH > Ozone dose > Br - > Inorganic Carbon
Order of importance for parameters that tend to decrease bromate formation:
DOC > NH3-N
Absolute effect on bromate formation:
pH > Ozone dose > DOC > Br - < NH3-N Inorganic carbon
II.1.4 Microbial inactivation
Microorganisms respond differently to disinfectants and a number of models have
been developed to describe their inactivation rate. The models are based on general
behavior observed in disinfection experiments (“shoulders,” “tailing”) and an
understanding of the mechanisms by which disinfectants inactivate microorganisms. The
relations depend on kinematic parameters that are determined via statistical analysis of
experimental data collected in batch reactors. The most commonly used models,
corrected to account for first order disinfectant decay, are presented in Table 15 (Gyürék
and Finch 1998). In all the expressions in Table 15 except the Chick expression, the
degree of disinfection, Ct, includes changes in disinfectant concentration. In the Hom
and Hom power law expressions for batch survival, is the incomplete gamma function,
91
defined as
(m, n k t) e z z m1dz0
n k t
(27)
Haas and Joffe (1998) proposed a method for developing inactivation relations for
use in continuous flow systems based on models developed for batch inactivation data.
Greene, Haas et al. (2001) demonstrated this procedure in their CFD simulation of
chlorine, chloramines and ozone disinfection of four microorganisms in a pilot scale
single-phase contactor.
Current practice and regulatory requirements assess reactor performance in terms
of “Ct” rather than by direct measurement of inactivation in water treatment. The Ct
approach acknowledges that the survival of organisms depends on the concentration of
disinfectant to which they are subjected (C) and the time over which they are subjected to
the disinfectant (t). Because ozone decays and is consumed during the disinfection
process, an average ozone concentration is used to calculate Ct. The contact time is
chosen conservatively as T10, the time for the first 10% of a conservative tracer to be
discharged from the reactor following the step introduction of the tracer to the reactor
inlet.
The Ct approach is practical given the difficulty of counting the myriad organisms
present in drinking water and given the time required to produce accurate counts, but
problematic given the variations encountered in disinfection process operations such as:
92
variations in reactor hydraulics due to operation at off-design conditions;
variations in water quality leading to changes in disinfectant demand or microbial
sensitivity to the disinfectant;
influence of initial microbial density on inactivation rate; or
strain-to-strain variations in resistance to disinfection.
Table 15: Commonly-used Disinfection Models
Modelname
Predicted batch survival function
0
lnN
NKineticparameters Rate
Chick k C t k NCk
Chick-Watson
k C 0
n
n k*1 exp n k* t k, n NCk n
Hommk C 0
n
n k m m, n k t k, n, m m N k C n
1 m
lnN
N 0
11
m
Powerlaw
1
x 1ln 1
x 1 k C 0n
n k*N 0
x1 1 exp n k t
k, n, x xn NCk
Hompowerlaw
1
x 1ln 1 x 1
mk C on
n k* m m, n k t N 0
x1
k, n, m, x
m
m
n
xxxn
Ckx
NNNCkm
110
1
1
93
Equally problematic is the tendency for the Ct approach, as it is currently
implemented for ozone contactors, to overestimate the required ozone dose or contact
time to achieve a given level of kill. Overestimating required ozone dose results in
excess costs and the potential for forming more disinfection byproducts than if a lower
ozone dose were used.
Ozone is the most potent chemical biocide studied by the U.S. EPA to date (Clark
and Boutin 2001). A summary of inactivation data generated by several researchers for
ozone disinfection is presented in Table 16. Giardia muris and Cryptosporidium parvum
exhibit a temperature dependent lag phase when exposed to ozone (von Gunten 2003b).
Table 16: Summary of Ozone Inactivation Data (Clark and Boutin 2001)
Organism
Ct
L
minmg LogReduction Conditions
Indigenous aerobicbacterial endospores
19 3 Filtered Ohio River water attemperatures between 23.6 and 25.2ºC
Polio virus 1.2 2 Filtered Ohio River water attemperatures between 23.6 and 25.2ºCand pH 7.6
Giardia muris 1.9 2 Unknown water source, temperature of5ºC and pH of 7
Giardia lamblia 0.55 2 Unknown water source, temperature of5ºC and pH of 7
Giardia muris 0.75 2 Filtered Ohio River water, temperaturebetween 23 and 24C and pH 7.65
Cryptosporidiumparvum
5 2 Conditions not described
94
Organism
Ct
L
minmg LogReduction Conditions
Cryptosporidiumparvum
6.56 2.5 Temperature of 25ºC, other conditionsnot described
Cryptosporidiumparvum
4 1.4 Filtered Ohio River water, temperaturebetween 23 and 24C and pH 7.65
The action of ozone on pathogenic organisms has been debated, with the debate
fueled by a wide variation in published values for rate constants of organisms of interest
in water treatment. In one camp are those who believe that direct action of ozone on
microorganisms is the dominant mechanisms of inactivation. In the second, indirect
action of ozone through generation of hydroxyl radicals is assumed to be the dominant
mechanism in inactivation. Based on comparison of inactivation rates in the presence of
dissolved ozone with inactivation rates for organisms exposed to known concentration of
hydroxyl radicals, von Gunten (2003b) states that the predominant mechanism for
inactivation is direct action of ozone, with hydroxyl radicals playing a minor role.
II.2 Experimental Investigations of Bubble Column Reactors
The many published experimental investigations of phenomena in bubble column
reactors can be grouped into:
mass transfer investigations and
95
hydrodynamics investigations.
II.2.1 Experimental Measurement of Mass Transfer in Bubble Columns
To date, bubble column mass transfer investigations have involved measurement
of dissolved gas concentration at discrete locations along the bubble column reactor.
Experiments are performed for a range of gas and liquid flow rates and, in some cases,
with different water qualities.
LeSauze (1993) performed tracer studies and estimated ozone mass transfer for a
4.2 m tall, 0.l5 m diameter bubble column. Ozone mass transfer rate estimates were
based on analysis of samples drawn from sample ports located at the reactor top and
bottom and three intermediate depths. The precise depths of the intermediate sample
ports are not provided. Tracer and ozone mass transfer experiments were conducted at
three superficial liquid flow rates (0.86, 1.42, and 1.97 cm/s), four superficial gas flow
rates (0.076, 0.087, 0.203 and 0.48 m/s) and for influent gas-phase ozone concentration
ranging from 0.463 to 2.142 g/m3). Rather than use ozone residual data for developing a
rate expression for ozone mass transfer, the authors used an empirical relation for ozone
mass transfer from a prior study and assessed several combinations of ideal reactor
models to determine the one which best fit measured ozone residual data. Based on their
results, the authors suggested the following criteria be used in design of ozone contactors:
for water disinfection, reactors approaching plug flow conditions yield continuous
residual and optimal performance;
96
for use of ozone in oxidation of dissolved matter, reactors hydraulics should approach
complete mixed performance;
for realistic reactors which must achieve both objectives, reactors should be designed
in tow stages: a completely-mixed stage whose effluent is the ozone residual required
for disinfection followed by a plug flow stage that facilitates contact between
disinfectant and microorganisms.
To ascertain the influence of water quality on ozone mass transfer and
disinfection performance, Owens (2000) measured the influent ozone concentration,
effluent ozone concentration and ozone concentration for samples drawn from 4 equally-
spaced intermediate ports in an ozone bubble column of 0.15 m diameter and 2.65 m
height. The contactor was operated in countercurrent mode at a liquid flow rate of 6.4
L/min and a gas flow rate of 0.64 L/min. Ozone mass transfer rate was not estimated
directly in this study; rather, CT values corresponding to the depths of each of the
intermediate ports were determined by numerical integration of measured residual ozone
concentrations and assuming liquid flow rate equal to superficial velocity. Bromate
concentration was also measured in samples drawn from the influent, effluent and
intermediate ports. The authors concluded that, for Ohio River water, there is a trade-off
between the log removal of Cryptosporidium parvum oocysts and production of bromate.
In a study which compared ozone and peroxone (water with dissolved ozone gas
and hydrogen peroxide) for pre-oxidation to improve filter performance (Tobiason et al.,
1992), ozone dissolved into raw water in a 3.05 m tall, 30.5 cm diameter bubble column
97
run in countercurrent mode. Net ozone mass transfer was estimated based on gas phase
measurements of ozone in the feed gas and off-gas. Experiments were performed at a
liquid flow rate of 37.8 lpm and a gas flow rate of 16.5 slpm and at ozone doses ranging
from 0 to 0.75 mg/L. No ozone mass transfer analyses were performed in this study.
Both ozone and PEROXONE were found to extend filter runs when used in combination
with coagulant doses typically used in treatment at the New Haven, CT drinking water
treatment plant.
In another pilot study investigating the difference between ozone and
PEROXONE, Scott (Scott et al., 1992) dissolved ozone into pilot plant filter effluent in
four 5.2 m tall, 15.4 cm diameter cylindrical bubble columns arranged in series. Contact
time (taken to be equal to the effluent ozone residual multiplied by T50) was varied
between 2.16 and 5.23 mg-min/L). As in other pilot studies, ozone mass transfer rate was
not directly calculated. Ozone residual in the effluent was seen to vary “unpredictably”
with given dose. The authors did not speculate as to the cause of these variations, though
they advised use of measured residual rather than applied dose for estimating disinfection
in ozone contactors. The variation seen in ozone residual has been observed in full scale
contactors (Schulz and Bellamy 2000) and is likely related to hydrodynamics and sample
acquisition.
II.2.2 High-Resolution Study of Bubble Column Hydrodynamics
Several experimental techniques have been employed for observation and
quantification of hydrodynamics in bubble columns. Though techniques are available for
98
observation of bubble motion in an ensemble of bubbles, these techniques have most
often been applied for measurement of liquid-phase motion. These techniques provide no
direct measurement of mass transfer rate or dissolved gas concentration.
Particle image velocimetry (PIV) consists of laser sheeting, image recording and
data processing (Chen and Fan 1992). Images can record the position of bubbles in the
plane of the laser sheet and, when the liquid phase is seeded with visible particles, the
position of the particles suspended in the liquid phase (Degaleesan et al., 2001). In image
processing, procedures must be developed for distinguishing individual bubbles and
particles and for tracking particles and bubbles from frame to frame. Because the liquid
phase is usually seeded with visible particles, this technique has, to date, only been used
in bubble columns with non-flowing liquid phase. Versions of PIV have been used to
measure spatial variations in gas hold-up in a bubble column with non-flowing liquid
phase (Delnoij et al., 1999), to measure spatial variations in gas hold-up and turbulence
intensity in a two-phase system (Liu et al., 2005) and to make general observations of
flow in a three-phase system with non-flowing liquid and solid phases (Chen and Fan
1992). PIV allows visualization of features that influence countercurrent mass transfer
(back-mixing and non-uniform hold-up) but does not allow direct measurement of the
effects of these phenomena on mass transfer.
Another experimental technique for quantifying hydrodynamics in bubble
columns is the computer-automated radioactive particle tracking (CARPT) procedure. In
contrast to PIV, CARPT experiments do not visualize flow on a single plane in the
99
bubble column. Rather, the positions of individual radioactive particles are tracked (in
three dimensions) as they are carried by the liquid phase. The advantage of this
technique over PIV is that it provides information on hydrodynamics in the entire reactor.
CARPT has been used to investigate the flow field (presence of circulation and
distribution of turbulence intensity) in bubble column reactors with non-flowing liquid
phase (Degaleesan et al., 2001).
II.3 Ozone Contactor Modeling
II.3.1 CFD Models
Four researchers have published papers on CFD ozone bubble columns modeling
studies. These studies are described below and summarized in Table 17.
In a study performed for the Metropolitan Water District of Southern California,
Henry and Freeman (1995) developed a finite element model of a full-scale ozone
contactor. The commercial code FIDAP (formerly licensed by Fluid Dynamics Inc.,
currently by Fluent Inc.) was used to perform a two-dimensional, two-phase simulation of
a proposed full-scale contactor. Bubbles were assumed to have fixed diameters of 3 mm
and were modeled via a Lagrangian approach. Details on gas boundary conditions are
not provided.
The CFD model was used to simulate a tracer study and results were compared
with experimental data. The authors report an average deviation of CFD study tracer E
curve values (expectation) of 6.8% from experimental values. The E curve (also called
100
the exit age or residence time distribution curve) is a plot of measured or predicted tracer
concentration as a function of time and normalized by intake tracer concentration. Plotted
experimental and computational tracer curves indicate the CFD model significantly over-
predicts dispersion. Having modeled tracer studies, the authors modeled potential design
modifications to the ozone contactor including:
Alternate water depth to contactor length ratios;
Alternate baffle gap spacing to chamber length ratios;
Addition of vanes, corner fillets and wall foils.
Sketches showing the baffle gap, vanes, fillets and wall foils are provided in Figure 15.
In general, greater water depths and wider baffle spacing gaps result in higher
T10:HDT. T10 is the time at which 10% of the tracer exits the contactor and HDT is the
contactor hydraulic detention time. Higher T10:HDT indicates more uniform contacting
of water with dissolved ozone and is generally desirable. Addition of vertical vanes in
the contactor (to direct flow passing through baffle gaps) had a pronounced effect on
RTD, increasing predicted T10:HDT by 8%. Fillets provided only minor improvement in
hydraulic performance. Adding wall foils produced a 4.8% increase in predicted
T10:HDT.
101
Figure 15: Ozone Contactor Design Modifications (Henry and Freeman 1995)
A progenitor to the commercial CFD code CFX was used to assess design
modifications to a full-scale ozone contactor employed at the Alton Water Treatment
Works, Anglian Water, UK (Murrer et al., 1995). The authors performed the study in the
hopes of developing an alternative to expensive, time consuming and complicated
experimental studies. A schematic diagram showing the contactor is found in Figure 16.
Few details of the CFD model are provided in the published results. The model
was three-dimensional and two-phase, though details on treatment of multiphase
momentum and mass transfer are not provided. The authors state that the model was
calibrated via modifications and comparison with pulse tracer studies, though it is unclear
what they take calibration to mean and what model parameters may have been adjusted.
102
Excellent correlation of simulated and experimental tracer curves is claimed without
reference to any quantitative measure of correlation.
Following successful calibration of the CFD model, the authors extended the
model to include ozone transfer between phases and ozone demand in the aqueous phase.
A bench-scale experimental study was performed to ascertain bubble size, rise rate and
growth rate. Employing these data, CFD simulations were able to predict ozone residual
in the full scale reactor accurately. Finally, the authors predicted the reactor performance
under varied operating conditions, with modified diffuser placement and with additional
baffling in the final chamber of the contactor. The CFD model predicted significant
improvement in reactor performance when the gas flow rate in the first bubble contacting
chamber (see Figure 16) was higher than in the second and when a baffle was added to
the last chamber in the reactor.
103
Figure 16: Murrer, Gunstead et al. (1995) Reactor Schematic
Cockx, Do-Quang et al. (1999) performed the most inclusive CFD study of an
ozone contactor to date. In the study, CFD was used to simulate two-phase flow, ozone
mass transfer and ozone decomposition in a full-scale bubble contactor. The contactor
modeled was comprised of seven chambers whose combined volume is 350 m3 and with
a capacity of 53,000 m3/day. A schematic diagram of the contactor is presented in Figure
17.
The authors used the finite volume CFD code ASTRID for analyses. An
Eulerian-Eulerian treatment of two-phase flow was employed with provisions made for
momentum and mass transfer between the phases. Momentum exchange between the
104
phases is calculated as
ML ap
1
2lCDVr Vr (28)
where ML is the mean volumetric momentum transfer to the liquid phase from the gas
phase for a control volume, ap is projected volumetric interfacial area (L2 projected
surface area per L3 reactor volume), l is liquid phase density, CD is drag coefficient
(described below) and Vr is the relative speed between the phases (the slip velocity). The
authors assumed ellipsoidal bubbles with attendant volumetric interfacial area of
ap 3
2
g
b(29)
where g is local volumetric gas fraction and b is the projected bubble diameter on a
horizontal plane. Without explanation, the authors selected a drag coefficient of 1.0.
Bubble diameter was assumed uniform and constant and equal to 3 mm. No mention is
made of bubble-induced turbulence (Sato and Sekoguchi 1975) and it is assumed the
authors did not account for that phenomenon.
105
Figure 17: Reactor Schematic for Cockx CFD Study
Mass transfer of ozone between the gas and aqueous phases, given as
Ll kLa (CL* CL ) (30)
where Ll is mean volumetric mass transfer to the liquid phase, kL is the interphase
transfer coefficient, a is volumetric interfacial area (L2 bubble surface area per L3 reactor
volume), CL* is the saturation concentration of ozone corresponding to the gas-phase
ozone partial pressure and CL is mean local aqueous ozone concentration. Without
providing insights into the reasons for their choice, the authors use the Higbie (Motarjemi
and Jameson 1978) relation for mass transfer coefficient:
106
a 6 g
db
; kL 2DO3
Vb
db
(31)
where DL is molecular diffusion (L2/T) for dissolved ozone in water. Direct use of the
Higbie relation is questionable, since it was developed for large bubbles with mobile
surfaces in pure water. The influent water is assigned an instantaneous ozone demand of
0.24 mg/l and aqueous phase ozone decay is assumed to follow first order kinetics with a
rate constant of 0.12 min-1.
Cockx compared results from the resulting CFD model with experimental tracer
study data and particle image velocimetry (PIV) data collected in a pilot study. The pilot
study data are not reported. RTD curves for experimental and simulated tracer studies
appear to agree well, through no statistical or quantitative measure of their agreement is
presented. Based on apparent success in simulating tracer experiments, the authors
simulated a modified reactor in which baffles were added to the chamber to inhibit short-
circuiting and promote slug flow. In CFD simulations of the modified reactor, Ct
(presumably at the reactor discharge) was increased 165%. In experiments (whose
details are not described) Ct was improved 114%.
In the most recent published ozone contactor CFD study, Huang, Brouckaert et al.
(2002) developed a model for a full-scale ozone contacting system. The ozone contactor
modeled in that study is a retrofit of a chamber whose primary use is water disinfection.
The contactor is located at the Wiggins Water Works, Durban, South Africa. It consists
of a static mixer, located immediately upstream of the contactor, in which ozonated air is
107
injected into the water stream and all ozone is assumed dissolved into the aqueous phase.
No data are presented to support the assumption that all ozone is transferred from the gas
phase prior to introduction of the water/gas mixture into the contact chamber. Ozonated
water is introduced into the contact chamber via an inlet located in the chamber bottom.
The contact chamber is of serpentine design and water exits the contactor via a weir.
Huang used the commercial CFD code FLUENT for numerical analyses and used
FLUENT’s preprocessor, GAMBIT, for developing a mesh. A - turbulence model was
employed and the presence of bubbles was approximated via augmented turbulence
intensity of the inlet stream. Only heuristic justification was provided for approximating
the gas phase in this manner. Inlet turbulence intensity was adjusted to provide the best
match between computational and experimental tracer studies. The inlet (located on the
contactor floor) was modeled as a Dirichlet boundary condition. The free surface was
approximated as a horizontal rigid lid. The outlet weir was approximated as a submerged
rectangular slot and a frictional loss coefficient was assigned to the weir to account for
head loss over the weir.
Experimental tracer studies were performed for the contactor with and without
gas injection. The presence of injected gas made a relatively minor difference in the
shape of the tracer curves. Computational tracer studies were performed and turbulence
intensity, defined as
IT
2
3
V(32)
108
was varied. In equation 1, IT is turbulence intensity (dimensionless), is turbulent
kinetic energy (L2/T2) and V is mean fluid speed (L/T).
The authors found that an inlet turbulence intensity ratio of 50% provided a better
match between experimental and computational tracer curves than an inlet turbulence
intensity ratio of 20%. This conclusion was based on qualitative comparison of
experimental and simulated tracer curves. The authors state that the good agreement
between simulated and experimental tracer studies validate their model and justify the
simplifications employed, especially their simplified treatment of two-phase flow.
Table 17: Summary of Ozone Contactor CFD Studies
Author Code andformulation
Two-phasemodel
Turbulencemodel
Masstransfermodel
Ozonechemistry
Inactivationmodel
(Henry andFreeman1995)
FIDAP/FE Eulerian-Lagrangian
- None None None
(Murrer et al.,1995)
CFX/FV Eulerian-Eulerian
Unknown Unknown Demand None
(Cockx et al.,1999) and(Do-Quang etal., 1999)
ASTRID/FV
Eulerian-Eulerian
- Higbie Instanta-neousdemand,1st-orderdecay
Chick
(Huang et al.,2002)
FLUENT5.5.14/FV
Modifiedinfluentturbulenceintensity
- None None None
109
II.3.2 Other Models
Ozone contactor modeling has historically been performed using one-dimensional
axial dispersion models or tanks in series models. These models have provided insights
into gross design principles and have provided a means for analyzing data collected in
laboratory and pilot scale plants but do not have an obvious role in detailed investigation
of bubble column phenomena or design of full scale contactors. Several ozone contactor
models are described below, with emphasis on their successes and limitations.
LeSauze, LaPlanche et al. (1993) modeled countercurrent ozone mass transfer in a
bubble column using three ideal reactor models and a fourth model in which portions of
the reactor were modeled via different models. The ideal reactor models employed were
a completely stirred tank reactor (CSTR) model, a plug flow reactor (PFR) model and an
axial dispersion model. In the hybrid model the portion of the reactor near the sparger
was modeled via an axial dispersion model with high dispersion, the middle portion of
the reactor was modeled as a PFR and the top portion of the reactor was modeled via an
axial dispersion model with a moderate level of dispersion. The hybrid model results
provided the best match with data collected in an experimental bubble column.
Zhou and Smith (1994) developed an axial dispersion model of a countercurrent
ozone bubble contactor and used the model to predict the performance of a bubble
contactor for varying liquid and gas flow rates and feed gas ozone concentrations. Mass
transfer coefficients were estimated via the Deckwer correlation (Table 12) and
corrections were made for aqueous phase ozone decay. The authors made a limited
110
number of comparisons of model outputs with experimental data and described the data
that would be required to perform more rigorous validation of the model.
Finally, Kim, Tomiak et al. (2002a) developed an axial dispersion model inclusive
of ozone mass transfer, ozone demand, ozone decay and microbial inactivation. The
resulting ordinary differential equations are presented below. Numerous assumptions
were made in development of this modeling, including first-order ozone decay, second
order reaction of ozone and natural organic matter (NOM), uniform steady bubble
diameter, uniform axial dispersion in the bubble column and Chick-Watson inactivation
kinetics (with n=1).
0
0
0
0
,2
21
,2
21
,,2
21
3
LNae
NOMLNOMaNOMNOM
e
L
H
gSH
g
NOMLNOMaLOaL
H
g
SLL
e
CNDzd
Nd
zd
NdP
CCDzd
Cd
zd
CdP
CK
C
S
N
zd
K
Cd
CCDCDCK
CN
zd
Cd
zd
CdP
(33)
In these expressions, z height above the column bottom, CL and Cg are liquid and gas
phase ozone concentrations, Da,I is Damkhöler number for the reaction in which species i
is consumed, N is number of microorganisms per unit volume, NS is Stanton number and
S is a stripping factor, defined as
111
L
g
U
UmS (34)
Auxiliary relations for bubble diameter, mass transfer coefficient, Henry’s law
constant and microbial inactivation rate were used to determine constants found in the
above equations and the resulting equations were solved simultaneously.
The authors compared predicted ozone transfer and microbial inactivation to
experimental data with generally favorable results. The authors cautioned strongly
against general application of this model to other contactors without careful examination
of parameter estimations. Application of this model to a full-scale reactor with three-
dimensional flow patterns would be problematic. Specifically, several assumptions used
in developing the axial dispersion model are invalid for the hydraulically-complex flows
encountered in full-scale reactors. Questionable or invalid assumptions include uniform
dispersion, uniform gas phase distribution in the reactor, and one-dimensional transport
within the reactor.
II.4 Other Bubble Contactor CFD Studies
As recounted below, researchers have applied numerous techniques in developing
CFD models for bubble contactors. In this section the major modeling choices for CFD
simulation of bubble columns are presented and examples of studies using various types
of models are described. The majority of the bubble contactor papers identified in the
literature were analyses of bubble columns in which gas was bubbled through stagnant
liquids and the authors were interested mainly in hydrodynamics, not mass transfer.
112
Several authors noted the lack of bubble column experimental data in the open literature
for comparison with CFD simulations (Mitra-Majumdar et al., 1998; Sanyal et al., 1999).
The same can be said for axially-resolved and radially-resolved mass transfer data. Thus,
in the short term validation of modeling approaches and exploration of submodels will be
a major hurdle for researchers simulating bubble columns with CFD.
In simulating a bubble column via CFD, the major choices that must be made are:
Treatment of two-phases (Eulerian-Eulerian, Lagrangian-Eulerian, Algebraic Mixture
Model or Direct Numerical Simulation);
Choice of steady or transient simulation;
Choice of domain (2-dimensional or 3-dimensional);
Turbulence model (-, -, large eddy simulation [LES] or perhaps others); and
Choice of submodels for interphase momentum transfer and mass transfer (perhaps
accounting for interactions of bubbles with each other), bubble size (perhaps
accounting for coalescence) and turbulent dispersion enhancement due to bubbles.
Among the numerous papers in the literature describing CFD simulation of bubble
contactors, several are reviewed below to illustrate these different approaches.
Ranade (1997) undertook CFD studies of bubble columns because, like Mitra-
Majumdar et al., he felt one-dimensional approaches lack generality (are applicable only
for designs and operating conditions for which experimentally-derived constants are
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valid). Studies were performed for air-water systems with bubbles whose diameter
varied from 3 mm to 8 mm. The objective of the work was to reproduce numerically the
tendency of bubbles to migrate toward the center of a cylindrical bubble column in
heterogeneous bubble flow. To account for this, the author resorted to an artificial, if
effective, device – the imposition of the following condition on bubble drag:
FD a br
R
1 2
(35)
In the above relation FD is the drag force on the bubble at radial coordinate r, R is the
bubble column radius and a and b are constants equal to 2.2 and 1.7, respectively. The
constants a and b were chosen to reproduce observed distribution of the gas phase in the
reactor and are believed to account for bubble-bubble interactions. The ratio of bubble
drag coefficient to diameter was chosen to be 290 m-1. Not surprisingly, the author
achieved good qualitative agreement with experimental values. The agreement was
assessed via graphical comparison of axial mean velocity and turbulence intensity and
radial gas phase holdup.
In a demonstration that CFD can be applied to increasingly complex bubble
column flows, Mitra-Majumdar, Farouk et al. (1998) developed a CFD model of two and
three-phase co-current flow of water, air bubbles and glass beads. An Eulerian-Eulerian
treatment of the multiple phases was used and both the gas and solid phases were treated
as dispersed phases. Both experiments and CFD simulations were performed and radial
and axial gas and solid phase holdups were compared with experimental data. In general,
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the two-phase CFD model predicted radial variation in gas phase holdup well, while the
three-phase model did not fare as well, perhaps due to the choice of drag model in the
three phase CFD simulations.
Pfleger, Gomes et al. (1999) performed CFD and experimental investigations of a
bubble column with stagnant water and air bubbles sparged into a rectangular channel.
The position of the sparger and gas flow rate were varied and two-dimensional and three-
dimensional transient simulations were performed. The commercial CFD code CFX 4.2
was used for the CFD simulations and the two-phase system was modeled as Eulerian-
Eulerian. Time steps were 0.01 seconds and the total simulated (real) time was 400
seconds. A fixed bubble diameter and drag coefficient were specified.
The authors noted a marked difference between two-dimensional and three-
dimensional simulations, with the three-dimensional calculations far better estimating
experimentally measured turbulence intensity and qualitative behavior (transient drift) of
the bubble plume in the column. The authors determined that the keys to performing a
tractable and realistic bubble column simulation were to use three dimensions and a fine
length scale. The - turbulence model employed for the liquid phase appeared adequate
for producing realistic results.
Eulerian-Eulerian and Algebraic slip mixture model two phase flow treatments
were compared directly in a study performed by Sanyal, Vásquez et al (1999). The
authors used the commercial CFD code FLUENT (Fluent, Inc., Lebanon, N.H., USA) to
perform transient, two-dimensional simulations of a circular cylindrical bubble column in
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which air was sparged into stagnant water. A single bubble diameter was chosen to
represent the bubble size distribution and bubble drag was calculated via a relation for a
single sphere dropping in an infinite fluid (the precise relation is not provided in the
paper). Time steps were 0.01 seconds for Eulerian-Eulerian simulations and 0.005
seconds for simulations using an algebraic slip mixture model two-phase treatment. The
turbulence model was - and a uniform grid (0.66 cm axial 0.5 cm radial)
approximated the geometry.
The authors found good agreement between results generated using both two-
phase models when bubbly flow was simulated but found significant difference when
churn turbulent flow was simulated (no mention is made of changes in bubble diameter or
coalescence for heterogeneous bubble flow). Both models tended to over predict the
centerline axial velocity. Though the authors did not draw this conclusion, this result is
consistent with the experience of Pfleger et al. (1999) and indicates that two-dimensional
bubble column simulations have limitations. However, Sanyal concluded that two-
dimensional axisymmetric models provide “good engineering descriptions” of bubble
column hydrodynamics and holdup. The authors indicated the need for better turbulence
modeling and prediction of turbulent diffusivity.
In a CFD simulation of a bubble plume in a cylindrical column whose diameter is
much greater than the plume diameter, Bernard, Maier et al. (2000) used a single-phase
flow code, MAC3D (Army Corps of Engineers Waterways Experiment Station,
Vicksburg, MS, USA) with source terms added to the momentum equation to simulate
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vertically-rising bubbles. The authors dub this approach the drift-flux model. The
advantages of this approach are obvious – single-phase calculations are much easier to
perform and require less computational effort than multiphase codes. MAC3D is a finite
volume code and a - turbulence model was employed for the liquid phase. Walls were
modeled as no-slip boundaries and the free surface was approximated as a rigid lid.
Bubbles were assumed to have a uniform diameter and plume geometry was imposed on
the solution. The model reproduced steady velocities in the bubble plume within a factor
of two and the authors believe the far-field mixing effects of a bubble plume in a
reservoir were well characterized. The authors indicated their intent to perform future in
which the model accounts for stratified liquids.
Large Eddy Simulation (LES) and - models were compared for Eulerian-
Eulerian simulation of bubble column flow by Deen, Solberg et al. (2001). Results from
CFD simulations were compared to experimental data and the two turbulence models
were compared. The bubble column in that study was a rectangular cross-sectioned
cylinder outfitted with a distributor plate with 49 holes of 1 mm diameter. Grid spacings
for the - turbulence model simulations were 101010 mm. Coarse (101010 mm)
and fine (4.7104.7 mm) grid spacings were used in LES simulations. Transient flow
was modeled and time steps of 0.01 sec and 0.005 seconds were used for the - and LES
simulations, respectively. Bubble diameter was uniform and steady and set equal to 4
mm. The drag coefficient was chosen to be 1.0 based on the computed value of Eötvös
number. The Sato model for enhanced turbulence (Sato and Sekoguchi 1975) was
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employed.
Comparison of profiles of simulated and experimental liquid axial velocity
profiles, axial gas velocity profiles, radial liquid velocity fluctuations and turbulent
kinetic energy profiles showed clearly that the LES turbulence model produced better
agreement between calculations and experiment. LES computations took 90 hours to
complete on a 4-processor, high-end workstation. No data are provided on the
computational requirements for the - simulations.
The Euler-Lagrange approach to two-phase modeling in a bubble column was
employed by Laín, Bröder et al. (2002). A comparison of the Eulerian-Eulerian and
Eulerian-Lagrangian approaches summarized from that paper is presented in Table 18.
Table 18: Comparison of Eulerian-Eulerian and Eulerian-Lagrangian Approaches
Approach Eulerian-Eulerian Eulerian-Lagrangian
Liquid phase Navier-Stokes equations withsource terms added for bubblemomentum transfer
Navier-Stokes like equationscoupled with Navier-Stokes likeequation for gas phase
Gas phase Newtonian equations of motionwith bubble-bubble interactionsvia collision models
Navier-Stokes like equationscoupled with Navier-Stokes likeequations for liquid phase
Appropriateapplications
Dilute two-phase flows andheterogeneous bubbly flows.
Dense flows. Validity isquestionable for very dilute flows(Laín et al., 2002)
Advantages Accounts for a spectrum of bubblesizes and allows modeling ofbubble break-up and coalescence
Computational efficiency. May beused to predict bubble coalescenceif bubbles are represented bymultiple dispersed phases (Olmoset al., 2003)
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CFD simulations and experimental results were compared for a bubble column
(air-water) with stagnant water and a membrane aerator. Based upon previous
experience, the authors used a distribution of bubble diameters (the precise distribution is
not stated) and calculated drag coefficient as:
CD
16Re1 Re 1.5
14.9Re0.78 1.5Re 80
48Re1 1 2.21Re
0.5 1.861015 Re4.756 80 Re 1500
2.61 Re 1500
(36)
where Re is Reynolds number based on the bubble diameter and magnitude of the
velocity difference between the bubble and liquid. Transient, two-dimensional
calculations were performed.
Time-averaged mean and fluctuating velocity profiles (axial and radial) were
compared with experimental values and good agreement was claimed. In general, the
authors determined that accurate modeling of bubble column flow with the Eulerian-
Lagrangian approach requires:
Inclusion of relevant bubble class sizes in the Lagrangian model;
Use of an appropriate relation for drag coefficient that distinguished between
Reynolds number regimes; and
Application of appropriate source terms in a - turbulence model to account for
interphase momentum transfer.
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III EXPERIMENTAL METHODS
Two types of laboratory experiments were performed in a bubble column
operated with countercurrent flow:
Residence time distribution (RTD) studies and
Ozone mass transfer visualization studies.
RTD studies generated data that allowed evaluation of column hydrodynamics
and characterization of mixing. These data were used to relate mixing intensity to
column operating conditions and in validation of the proposed CFD model. Ozone mass
transfer visualization studies enabled quantification of spatial variations in mass transfer
in the reactor and were also used in CFD model validation.
As described in the literature survey, numerous experimental methods for
investigation of hydraulics and mass transfer in bubble column reactors have been
employed in prior studies. None of these methods were deemed appropriate for
generating data about mass transfer at the fidelity desired in the current study.
For example, in all prior ozone bubble column mass transfer studies (Scott et al.,
1992; Tobiason et al., 1992; Mariñas et al., 1993; Owens et al., 1994; Saberi et al., 1995;
Owens et al., 2000; Kim et al., 2002a; Kim et al., 2002b; Charlton 2003) ozone mass
transfer rate was estimated based on discrete measurements of ozone residuals at the
bottom and top of the reactor or at six or fewer intermediate positions along the reactor.
These measurements allowed mass transfer rate estimates, but were not sufficiently
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resolved to relate mass transfer to hydrodynamics and did not result in expressions for
mass transfer that could be scaled. Other experimental studies such as those employing
phase-Doppler anemometry (PAD) (Laín et al., 1999), particle image velocimetry (PIV)
(Chen and Fan 1992; Delnoij et al., 1999; Liu et al., 2005) or computer-automated
radioactive particle tracking (CARPT) (Chen et al., 1999; Degaleesan et al., 2001)
provided highly-resolved data on distribution of bubbles or flow field, but did not yield
information about mass transfer. Additionally, since the PIV and CARPT techniques
require seed of particles in the liquid phase, they are generally performed for bubble
columns with non-flowing liquid phase.
Because the techniques outlined above could not provide mass transfer data at the
resolution desired, a novel technique for obtaining mass transfer data was developed.
This technique is described in detail in III.3. The only prior study that employed a
similar technique (image analysis of images taken of flow in a countercurrent flow
bubble column reactor) (Rice and Littlefield 1987; Baird and Rao 1998) investigated
dispersion, not mass transfer.
III.1 Experimental Apparatus
Experiments were performed in the 15.2 cm diameter, 1.83 m tall glass bubble
column reactor shown in Figure 18 and depicted schematically in Figure 19 and Figure
20. As reported in the literature review of this dissertation, all pilot and laboratory
continuous flow bubble column ozone contactors studies found in the literature employed
circular cylindrical reactors (Roustan et al., 1987; Scott et al., 1992; Tobiason et al.,
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1992; LeSauze et al., 1993; Mariñas et al., 1993; Kim et al., 2002a; Kim et al., 2002b;
Charlton 2003). The reactors used in these prior studies differed only in their inlet and
outlet configurations, diffuser type and location, and operating conditions. The reactor
chosen for the current study was selected because it was similar to reactors used in prior
pilot studies of ozonation in bubble columns (allowing easy comparison of performance
with reactors used in prior studies) and because a suitable column was available for use at
Drexel following relatively minor modifications.
Figure 18: Experimental Reactor Photograph
122
The column’s liquid feed is a mixture of tap water and stock solution. For tracer
studies the stock was a dilute solution of sodium chloride. In ozone visualization
experiments the stock solution was a 100% dilution of potassium indigo trisulfonate dye
reagent (described below). The tap water stream was metered via a rotameter and the
stock solution stream was delivered by a metering peristaltic pump (Fisher Scientific
[provide model number]). A 30 cm in-line helical static mixer mixes the two liquid
streams approximately 60 cm upstream of the introduction of the liquid stream into the
reactor. The liquid stream is introduced to the reactor through two ports (0.64 cm
diameter) in the bottom of the reactor collar. The collar was packed with 7 mm beads
that dissipate the inlet liquid stream momentum and promote uniform flow into the
bubble column. Liquid flows downward in the bubble column, exiting the reactor via
four symmetric discharge ports in the bottom of the reactor. The bottom of the reactor is
packed with 7 mm glass beads to promote uniform flow and reduce the impact of
discharge design on flow in the reactor.
Gas flows into the reactor via a 2.5 cm spherical fine bubble diffuser located
approximately 5 cm above the reactor bottom, as depicted in Figure 21. In tracer
experiments the gas feed is compressed air and in ozone mass transfer visualization
experiments the gas feed is ozonated compressed air. A rotameter measures gas flow
feed rate. Off gas is vented from the top of the reactor. For experiments in which
ozonated air is bubbled in the reactor, the off-gas is bubbled in a closed flask under a
chemical fume hood (to allow measurement of off-gas ozone concentration). Discharge
123
from the closed flask is then fed to a solution of sodium thiosulfate to ensure destruction
of residual ozone.
Bubblecolumn
To drain
In-linemixer
Ozonedestruction
Dischargegas phase
ozonemeasurement
Stocksolution
Liquid flow path
Gas flow path
Rotameter
Tapwater
Gas feed
Gas discharge
123.4
Liquid feed
Liquid discharge
Spherical diffuser
Intake collar
Figure 19: Laboratory Bubble Column Schematic Diagram (not to scale)
124
Figure 20: Reactor Schematic Diagram, Scale Drawing
Figure 21: Scale Drawing of Laboratory Column Bottom
125
III.2 Residence Time Distribution Studies
Step tracer experiments were used to generate data for residence time distribution
analyses. Stock solutions of sodium chloride tracer were mixed to provide a tracer
concentration of 500 mg/L in the reactor liquid feed. This concentration was chosen
because it provides a sufficient variation in liquid feed conductivity for accurate
measurement of tracer breakthrough but does not have a large enough difference in
density from that of tap water to influence hydrodynamics (Bartrand et al., 2005). Salt
concentration was measured as conductivity with a VWR dip cell conductivity meter
(model 2052). A plot showing conductivity measured by the conductivity probe as a
function of salt concentration is presented in Figure 22. Because conductivity is a linear
function of sodium chloride concentration over the concentration range used in tracer
experiments, conductivity measurements were used instead of salt concentrations in
residence time analyses.
126
CNaCl (g/100 mL)
0 1 2 3 4 5
Con
duct
ivit
y(m
S)
0
10
20
30
40
50
60
70
Figure 22: Conductivity Probe Calibration
Prior to step tracer experiments, the liquid stock was tap water and the reactor was
operated at steady gas and liquid flows for at least 4 theoretical hydraulic residence times.
At the beginning of tracer experiments (time = 0 sec) the liquid stock solution was
changed from tap water to sodium chloride solution. Samples were taken from the liquid
discharge line approximately 8 cm downstream of the reactor discharge at 15 second
intervals. After approximately 4 theoretical hydraulic residence times, the stock solution
was switched to tap water and samples were taken for an additional 4 theoretical
hydraulic residence times. Both step-up and step-down experiments were performed so
that effects of tracer density on the tracer curve might be identified. A typical tracer
curve is shown in Figure 23.
127
0.0
0.2
0.4
0.6
0.8
1.0
0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0
t /
F
Figure 23: Typical Tracer Curve
In Figure 23, as in subsequent analyses, tracer data are normalized and presented as an
“F” curve, where
backgroundfeed
backgroundtracer
CC
CCF
(37)
and time is non-dimensionalized by theoretical hydraulic residence time, tH. In equation
35, Ctracer is the conductivity immediately downstream of the reactor discharge, Cfeed is
the conductivity at the reactor intake and Cbackground is the background (tap water)
conductivity.
Residence time distribution data (F, ) were fit to the five residence time
distribution models depicted in Figure 24. The single stream N-CSTR and 1-dimensional
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ADR (advection dispersion reaction) models (Figure 24(a) and Figure 24 (c)) were
chosen because of their widespread use in reactor analysis (e.g., LeSauze et al., 1993;
e.g., Kim et al., 2002a). Parallel stream models (Figure 24(b) and Figure 24 (d)) were
chosen to account for the presence of two streams in two-phase flow – one associated
with downward flow of liquid outside the bubble plume and a second associated with
downward flow of liquid within the bubble plume. The cell backflow model (Figure
24(e)) was chosen because entrainment of liquid into the bubble plume was observed
during flow visualization and because of reported successes modeling two phase flow
with the cell backflow model (Nauman and Buffham 1983; El-Din and Smith 2001(b)).
a. N-CSTRmodel
b. ParallelN-CSTRs
c. 1-D ADRmodel
d. Parallel1-D ADRs
e. Cellbackflowmodel
Q
qQ + q
Q Q
x Q (1 – x) Qx Q (1 – x) Q
Figure 24: RTD Model Schematic Diagrams
129
It can be shown that the residence time distribution of a step tracer for an N-
CSTR reactor model is given by the equation (Haas et al., 1997):
Dt
t
DttE
H
H
H
H
4
1
exp
2
1
2
(38)
where D is dispersion, H is mean hydraulic residence time, and t is time. This
distribution depends upon two parameters, D and H. Rather than reporting dispersion
directly, mixing is usually reported via the dimensionless parameter Peclet number,
defined as
D
LUP L
e (39)
where UL is liquid superficial velocity (volumetric flow rate divided by reactor cross
sectional area), and L is characteristic length (reactor height for bubble column reactors).
The inverse Gaussian function provides an approximation for the residence time
distribution for the axial dispersion model. This distribution is a function of two
parameters, mean hydraulic residence time and variance of the inverse Gaussian
distribution, , and an approximation to the distribution is given by (Haas et al., 1997):
t
t
ttE
2exp
2
2
3(40)
The parallel stream models are linear combinations of equations 38 and 40 of the
130
form
tEtEtE 21 1 (41)
where is an additional parameter that provides the distribution of mass flow in the
parallel reactors. The parallel reactor distributions are functions of 5 parameters.
Although approximations to the cell backflow model have been proposed in the
literature (Retallick 1965) they are accurate over small ranges in the number of cells and
the amount of backflow between cells (q) and use of the full model equations for
modeling two phase flow is recommended (Nauman and Buffham 1983). Consequently,
best fit model parameters for the cell backflow model were determined by comparing
numerical solutions of the cell backflow model equations to experimental measurements.
III.3 Ozone Mass Transfer Visualization Studies
III.3.1 Overview
The objective of ozone mass transfer visualization experiments was to establish
steady flow conditions and obtain a digital photograph showing the distribution of a
reactive dye in a reactor.
Ozone mass transfer studies proceeded as follows:
1. Air was sparged into the reactor at a steady rate and off-gas from the head space was
vented through tubing and bubbled in water from a Milli-Q water system (Millipore
Intertech, Bedford, MA).
131
2. A mixture of reactive dye (buffered solution of potassium indigo trisulfonate) and tap
water was introduced to the reactor at a steady rate.
3. As dye filled the reactor, samples were taken from the reactor discharge at two
minute intervals. Dye concentration was determined from these samples via a
spectrophotometric measurement at 500 nm in a Barnstead/Thermoline
Spectrophotometer, model 340.
4. After at least 4 theoretical hydraulic residence times, steady conditions were assumed
to exist and the dye concentration was assumed uniform. While the reactor was being
filled with dye solution, water samples were taken from a sample port approximately
8 cm downstream of the reactor discharge at 2 minute intervals. After the completion
of experiments, the dye concentration in the samples was measured and used to
confirm that steady conditions had been achieved.
5. The ozone generator (shown in Figure 19) was switched on at a chosen voltage. The
voltage was chosen to ensure that enough ozone was supplied to the column to ensure
a significant difference in dye color between the top and the bottom of the column,
but not so much ozone that all the dye was decolored prior to discharge from the
column.
6. The liquid feed rate, gas feed rate and ozone generator voltage were held steady for at
least three reactor theoretical hydraulic residence times, during which time the ozone
decolored the dye and a quasi-steady distribution of dye was established in the
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reactor. The dye distribution was quasi-steady (rather than steady) because
turbulence in the reactor liquid flow caused fluctuating dye concentrations throughout
the reactor.
7. During the dye decoloration process, digital photographs were taken of the reactor at
2 minute intervals (details of the photographic setup are provided below) and samples
were withdrawn from the sample port downstream of the reactor discharge at 2
minute intervals. The digital photographs were used for calculating ozone mass
transfer rate and the samples were used to verify that quasi-steady conditions had
been established.
8. The liquid discharge temperature was noted and the water feed, gas feed and ozone
generator were turned off.
9. The ozone concentration in the water through which the off-gas was bubbled was
determined using the indigo trisulfonate method (American Public Health Association
1998).
10. The reactor was refilled with tap water and digital images of the reactor (with no dye
or bubbles) were taken. These images were used to remove variations in background
lighting from the images taken of indigo dye at quasi-steady distribution.
Important components of these steps are described in detail below.
III.3.2 Indigo Dye Solution Composition and Preparation
The dye used in ozone mass transfer visualization experiments is a buffered
133
solution of indigo potassium trisulfonate. Indigo trisulfonate is shown in Figure 25. In
solution, the carbon double bond of indigo trisulfonate reacts rapidly and preferentially
with ozone, decoloring the molecule (Bader and Hoigné 1981). One mole of ozone is
consumed per mole of indigo trisulfonate decolored. To determine whether tap water
contained constituents that interfered with the ozone-indigo dye reaction the indigo dye
method was used to measure the ozone concentration in a samples diluted with milli-Q
water and tap water. Ozonated air was bubbled into mill-Q water for 15 minutes (until a
steady ozone concentration was established) and 20 mL samples were transferred to 4
flasks containing 10 mL of indigo dye reagent. Two of the flasks were filled to 100 mL
with milli-Q water and two were filled to 100 mL with tap water. Absorbance at 500 nm
was determined via spectrophotometer. Experiments were conducted at 3 ozone residual
concentrations. In all cases there was no difference between absorbance (and ozone
concentration) between the samples diluted with tap water and those diluted with milli-Q
water. This indicated that tap water consitutents did not interfere with the ozone-indigo
reaction and that no treatment of tap water was necessary prior to use in ozone mass
transfer visualization experiments.
134
Figure 25: Indigo Trisulfonate Structure and Daughter Products
Prior to performing ozone mass transfer visualization experiments, test runs were
performed in which indigo dye was fed to the reactor at known concentrations and flow
rates and the ozone generator was operated at a range of voltages. These test experiments
identified a range of indigo dye concentrations and ozone generator voltages that
produced significant dye without causing complete decoloration anywhere in the reactor.
decoloring was observed but the discharge water was not completely decolored.
135
III.3.3 Photography Methodology
The setup for recording digital images was developed to
Provide uniform lighting of the reactor;
Provide images that spanned as much of the reactor as possible while still providing
high resolution;
Ensure photographs taken in different experiments were taken under the same
conditions.
Backlighting was used to provide uniform illumination of the reactor. The
lighting setup is shown in Figure 26.
The light sources were two high-temperature fluorescent lamps, 2.44 m (8 ft) tall,
mounted on the frame holding the bubble column. Because the lamps extended above
and below the reactor, variations in lighting along the reactor length were relatively
minor. The greatest variations in lighting occurred at the reactor top and bottom, where
light was partially blocked by the horizontal PVC sheets supporting the column. The
camera (Nikon Coolpix 8700, Nikon Corporation, Tokyo, Japan) was positioned 1.68 m
(66 in) from the front of the reactor. This position was chosen to maximize the reactor
height visible with zero zoom.
136
Figure 26: Mass Transfer Visualization Experiment Lighting
III.3.4 Development of Indigo Dye Color Calibration Curve
Prior to performing the steps outlined above, the relationship between the color
recorded in digital images and the indigo dye concentration was established. This
relationship was established by
filling the reactor with solutions of indigo reagent diluted with tap water,
taking samples and digital photographs of the reactor filled with dye,
plotting the dye concentration against the absorbance of the dye (measured via
137
spectrophotometer at 500 nm),
processing digital images to account for variations in background lighting and
plotting mean color of digital images against indigo dye concentration.
Experiments were performed at 6 indigo trisulfonate concentrations. The highest
concentration was chosen to be higher than any concentration that would be encountered
during ozone mass transfer visualization experiments.
Image processing consisted of:
Subtracting an image of the reactor filled with a known dye concentration from an
image of the reactor filled with tap water (the background).
Inverting the color of the resulting image.
Cropping the image to include only the reactor.
Removing the glass manufacturer’s mark by “cloning” an area immediately above the
mark over the black lettering.
Converting the image from 32-bit RGB JPEG image to an 8-bit (grey scale) TIF
(tagged image file) format.
Determining the mean pixel value and mode pixel value for the 8-bit image.
Image processing was performed using the public domain image processing software
ImageJ, version 1.34s (Rasband 2005). Processed digital images showing the dye color
138
at 6 dilutions are presented in Figure 27.
(a) 0.64 mg/L (b) 1.28 mg/L (c) 2.57 mg/L (e) 5.13 mg/L (f) 6.42 mg/L(d) 3.85 mg/L
Figure 27: Pixel Color Calibration Images
Histograms showing distribution of pixel color for the images shown above are
shown in Figure 28. The abscissas of the plots in Figure 28 are the pixel color (in 8-bit
grayscale). A pixel value of 0 indicates a completely black pixel and a pixel value of
256 indicates a completely white pixel. The histograms exhibit sharp peaks at distinctly
different pixel values over the range of indigo dyes examined. These sharp peaks at
139
distinct colors indicate that pixel color is a reliable indicator of indigo dye concentration.
Calibration of indigo dye concentration with pixel color is described below.
0.64 mg/L 1.28 mg/L0.64 mg/L0.64 mg/L 1.28 mg/L1.28 mg/L
2.57 mg/L 3.85 mg/L2.57 mg/L2.57 mg/L 3.85 mg/L3.85 mg/L
5.13 mg/L 6.42 mg/L5.13 mg/L5.13 mg/L 6.42 mg/L6.42 mg/L
7.70 mg/L7.70 mg/L
Figure 28: Calibration Image Histograms
140
A plot of absorbance at 600 nm versus indigo trisulfonate concentration for
dilution of indigo reagent in tap water is presented in Figure 29. The linear dependence
of absorption on indigo trisulfonate concentration indicates that:
The constituents of tap water do not significantly alter the absorbance of solutions of
indigo trisulfonate at 600 nm, and
Absorbance at 600 nm is a linear function of indigo trisulfonate concentration.
0
1
2
3
4
5
6
7
8
9
0 0.1 0.2 0.3 0.4 0.5 0.6
Indigo trisulfonate concentration (mg/L)
Ab
sorb
an
ce
Data
Least Squares Fit
Figure 29: Variation of Absorbance with Indigo Concentration for Indigo ReagentDiluted with Tap Water
141
Plots showing pixel value mean and mode for the images shown in Figure 27 and
Figure 28 versus known indigo dye concentration are presented in Figure 30. Curves
were plotted for images with and without the background subtracted and for the mode
and mean of the pixel values. Note that images are 8 bit gray scale. As such, pixel color
ranges from 0 to 256, with 256 corresponding to white (0 indigo dye concentration) and 0
corresponding to black. The curves corresponding to images with the background
subtracted are offset from those in which the background was not subtracted. This
indicates that the subtraction of the background pixel color does not affect the final image
color (monochromatic blue in RGB channels). Two important observations can be made
based on Figure 30:
For all curves, the variation in mean and mode of the pixel color is linear with indigo
dye concentration and
over the concentration range expected to span the concentrations during experiments,
there is a significant change in pixel color intensity.
These observations indicate that the pixel color intensity is a sensitive indicator of
indigo dye concentration and that a calibration curve relating pixel intensity to indigo dye
concentration may be developed. The calibration curve based on mean pixel color with
the background subtracted and is shown as a solid line in Figure 30.
142
0
50
100
150
200
250
300
0 1 2 3 4 5 6 7
Indigo Trisulfonate Concentration (mg/L)
Pix
elC
olo
r(8
bit
;0
=B
lack
,2
56
=W
hit
e)
Pixel color mean, background subtracted
Pixel color mode, background subtracted
Pixel color mean, background not subtracted
Pixel color mode, background not subtracted
Calibration curve
r2 = 0.985
Figure 30: Pixel Color Calibration Curve
143
IV NUMERICAL METHODS
IV.1 Mathematical Model
A two-phase model (Eulerian-Eulerian) is employed for the numerical solution of
the gas/liquid flowfields and phase distributions. In this model, the phases are modeled
as uniformly mixed within a given mesh element and the volume occupied by phase in
that mesh element is denoted . In the current two phase study, L is liquid volume
fraction, G is gas volume fraction and G + L = 1.0.
Assuming no source terms for the liquid and gas phases and no mass transfer
between phases due to phase change, the two-phase model continuity and momentum
equations are:
0
V
t
(42)
and
FVVPVVV
t
T (43)
where , V, P and are the density, velocity, pressure and viscosity of phase ,
respectively, and F is the interfacial force acting on phase due to the presence of the
other phase. For the current problem, the only interfacial forces of significance are drag
force and interphase turbulent dispersion force and
TD FFF
(44)
144
where DF
is the interfacial force due to drag and TF
is interfacial force due to turbulent
dispersion.
The drag component of the interfacial force term is given as
VVAC
F DD
8
(45)
where CD is drag coefficient, A is the net interfacial area between the phases and V
and
V
are the velocities of phases and . The Grace relation was chosen for drag
coefficient because bubbles were observed to be elliptical and dispersed. The Grace
drag coefficient (Clift et al., 1978) is:
LT
B
DU
dgC
23
4(46)
where g is gravitational acceleration, dB is mean bubble diameter, is the difference in
density between the phases, L is liquid phase density and UT is bubble terminal rise
velocity, given by
857.0149.0 Kd
UBL
LT
(47)
In the terminal velocity expression, is the Morton number (a fluid property) given by
32
4
L
L g (48)
145
where is surface tension and K is given by
3.5942.3
3.59294.0441.0
751.0
BB
BBK (49)
In equation 20, B is given by
14.0
149.0
3
4
ref
LEoB
(50)
and Eo is the Eötvös number, given by
2
bdg
Eo
(51)
Turbulent dispersion force is given by
L
L
G
G
Lt
Lt
dTD
T CCF
,
,
(52)
where CTD is an empirical constant (taken to be 1.0 in the absence of data for turbulent
dispersion force in countercurrent flow), Cd is drag coefficient (described above), t,L is
turbulent viscosity, t,L is liquid turbulent Schmidt number (taken to be 0.9) and G and
L are the gas and liquid phase volume fractions, respectively.
The two equation turbulence model (-) for the continuous (liquid) phase is
LLtLL
k
Lt
LLLLLLL PkUt
,
,
(53)
146
2,
,
LLtL
Lt
LLLL PUt
(54)
In equations 46 and 47, is the turbulent kinetic energy, is the characteristic turbulence
frequency, t,L is the liquid phase turbulent viscosity and the constants , ', k, and
are 0.075, 0.09, 2, 2 and 5/9, respectively. The liquid phase turbulent viscosity is
modeled using the Sato particle enhanced turbulence model (Sato and Sekoguchi 1975),
given in equation 48:
ptstLt ,,, (55)
where t,s is the conventional shear-induced turbulent viscosity and t,p is a particle
induced component of turbulent viscosity given by
LGbgLppt UUdC
,, (56)
and C,p is given a value of 0.6. The term Pt,L in equations 46 and 47 is the turbulence
production due to viscous forces, calculated as
LtT
tLt UUUUUP
33
2, (57)
The dispersed (gas) phase turbulence is modelled using a zero equation model in
which gas turbulent viscosity is proportional to liquid phase turbulent viscosity:
gt
Lt
L
GGt
,
,
,
(58)
147
where t,g is a turbulent Prandtl number relating the dispersed phase kinematic eddy
viscosity to the continuous phase kinematic eddy viscosity. In calculations, t,g was
assumed to equal 1, the standard value used in the absence of detailed turbulent kinetic
energy measurements.
The governing equation for transport of a conservative scalar quantity (tracer) in
the continuous (liquid) phase is given as
T
T
T
LTLLTLTL CSc
DUCCt
,
(59)
where CT is volumetric concentration of the tracer, DT,L is diffusivity of the tracer in the
liquid phase and ScT is turbulent Schmidt number. Because there is no mass transfer of
the tracer to the dispersed phase, there is no scalar transport equation for the dispersed
phase.
Dirichlet inlet boundaries were specified for water (at the top) and air (at the
bottom). A degassing boundary condition for the gas (no slip for the liquid phase, sink
term for the gas phase) was specified at the top of the reactor. In the laboratory reactor
the top of the reactor is a free surface and gas leaves the water at the free surface and
flows through a sealed plenum and escapes the plenum at a port located in the center of
the plenum top. Four pressure boundaries, located in the bottom of the column, make up
the water discharge boundary. In the laboratory reactor, the region between the sparger
and water discharge is packed with 7 mm glass beads. This volume is simulated in CFD
148
as a porous volume with transmissivity of 0.01 cm2. The transmissivity was estimated
using the Karman-Cozeny relation.
Simulations were started as steady state and results from steady simulations were
used as initial conditions for transient simulations. It was found that the following initial
conditions yielded a relatively fast (within 500 iterations) convergence to an rms (root
mean square) residual of 1×10-4 for all variables:
Uniform gas velocity equal to the predicted single bubble terminal rise velocity;
Uniform downward liquid velocity equal to the water volumetric flow rate divided by
the reactor cross sectional area.
Small gas volume fraction, uniform throughout the reactor.
IV.2 Numerical Model
The governing equations described in the earlier sections were solved numerically
for specified initial and boundary conditions with the commercial finite volume CFD
package CFX (ANSYS Europe Ltd. 2004) on a 3-dimensional unstructured mesh. Mesh
density was chosen based on a grid resolution study and generated to provide high
resolution at column walls and near the diffuser.
To assess the grid resolution, gas volume fraction along the column diameter
shown in Figure 31 was calculated at three mesh densities (coarse, medium and fine). In
grid resolution studies, steady flow was assumed, the gas phase was monodisperse with a
mean bubble diameter of 2.5 mm and a - turbulence model was employed. As
149
described below, steady flow is reasonable to assume when the bubble column is
perfectly vertical. When a slight lean (< 0.5º from vertical) is included, the bubble plume
is not steady in the center of the column and a transient simulation is required.
The coarse, medium and fine density grids had 140,000, 372,000 and 712,000
tetrahedral elements, respectively. In grid resolution studies the gas and liquid flow rates
were 2 L/min and 6.6 L/min. Results from the grid resolution study are presented in
Figure 32.
Because differences in the gas fraction profile were minor between the medium
and fine meshes, the mesh used in the present study is a refinement of the medium
density mesh. Prism elements were added to the medium mesh at the column walls and
the grid was refined locally in the vicinity of the sparger, water intake and the top of the
column (where water enters the column from the intake section). The resulting grid has a
total of 470,000 tetrahedral and prismatic elements.
150
Figure 31: Diameter Along which Grid Resolution Study was Performed
151
Figure 32: Gas Volume Fraction Profiles
A second-order upwind transient scheme with relatively small time steps (0.05 s)
was required to achieve convergence to an RMS residual of 1×10-5 within 10 iterations
per time step. To produce representative “quasi-steady” results, calculations were
performed for approximately 10s of simulation time, after which variations in bubble
plume shape became minor and bubble plume was seen to rotate in the column, though
not with a fixed period.
IV.3 Model Validation
Based on the observations of Rice and Littlefield (1987) and observations in the
laboratory, it was noted that minor misalignments of the column (of less than 0.5° off
152
vertical) or its components (e.g., sparger locations) can drastically change gas and liquid
flow and mixing. Despite efforts at leveling the column, locating the diffuser in the
column center and ensuring even flow through inlet and discharge ports, it was surmised
that perfect alignment of the column was unlikely. So the CFD model included a slight
(0.25°) vertical tilt. In the absence of this tilt, CFD predicted a perfectly symmetric
bubble plume. When the tilt was included the plume exhibited the asymmetric plume rise
observed in bubble column experiments. Specifically, the plume tended to migrate
toward the column wall and spiral as it ascended.
The countercurrent flow model was validated using tracer data (described below).
In the CFD model, a non-reactive, conservative tracer was introduced as a step feed in the
liquid phase at time 0s and the concentration of the tracer at the reactor discharge was
calculated at regular time intervals. The CFD model reactor discharge is shown in Figure
21. This study is referred to as a “virtual tracer study.”
Gas flow rate and liquid flow rate for the virtual tracer study were 2 L/min and
6.6 L/min, respectively. A plot showing normalized experimental tracer concentration
(F) and virtual tracer normalized concentration versus normalized time (t / tH) is
presented in Figure 33. The virtual tracer curve shown in Figure 33 is a plot of
instantaneous tracer concentration, area-averaged at the reactor discharge. The definition
of normalized tracer concentration is given in equation 37 (repeated below).
BackgroundFeed
BackgroundTracxer
CC
CCF
(37)
153
The CFD model reproduced measured residence time distribution data reasonably
well, predicting a slightly earlier breakthrough than that experimentally observed and
matching experimental data more closely at later times. In Figure 33, the CFD model
(the solid line) shows greater variation than the experimental data (symbols). This is
because the CFD model was “sampled” at 1 second intervals and via a point
measurement, whereas the experimental tracer studies used samples taken at 15 second
intervals and requiring approximately five seconds to draw. The agreement between
observed and predicted RTDs is considered excellent given the complexity of the flow
and the use of a two-equation turbulence model.
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7
t / t H
F
Numerical
Experimental
Figure 33: CFD Model Validation
154
V COUNTERCURRENT FLOW HYDRODYNAMICS INVESTIGATIONS
Experimental and numerical studies performed are summarized in Table 19. As
described above, tracer studies entailed introduction of a step input of sodium chloride
tracer at the reactor inlet and monitoring the conductivity of water at the reactor
discharge. Conductivity is a linear function of salt concentration over the concentration
range used in these studies. Tracer studies generated data for calculation of Peclet
number and characterizing dispersion. Tracer studies were performed at a single liquid
flow rate (6.6 L/min) and a range of gas flow rates chosen to span the ideal bubbly flow
regime.
Table 19: Countercurrent Flow Hydrodynamics Experimental and NumericalStudies
Study Liquid flow rate(s)(L/min)
Gas Flow Rate(s)(L/min)
FlowVisualization
6.6, 10.5, 13.5 0.4, 0.7
ExperimentalTracer
6.6 0, 0.5, 1.0, 1.5, 2.0,2.2, 2.4, 3.0, 3.5
CFD Studies 6.6, 13.5 0.4, 1.0, 1.5, 2.0, 2.5
In flow visualization studies, rather than a salt tracer, a non-reactive dye was
introduced to the reactor as a step function. Flow visualization studies were performed at
two gas flow rates (0.4 and 0.7 L/min) and liquid flow rates of 6.6, 9.0 and 12.0 L/min.
Flow visualization studies showed phenomena related to early breakthrough of tracer.
155
V.1 Bubble Plume Behavior and Flow Visualization
As gas flow rate was increased, the behavior of the bubble plume changed
significantly, though no increases in bubble break-up or collisions were observed. At a
low gas flow rate (0.5 L/min) and a liquid flow rate of 6.6 L/min, the plume rises
vertically and increases in diameter with height, as shown in Figure 34(a). Analysis of
high-resolution digital images indicates bubbles range in shape from nearly spherical to
oblate and bubbles tend to ascend in a spiral or zigzag path. At a higher gas flow rate
(2.5 L/min), the bubble plume rotates while rising, tending to migrate away from the
column centreline and toward the wall as shown in Figure 34(b). At some distance above
the sparger (typically between 0.6 and 1 m), the plume expands to fill the entire column.
b) High gas flowrate
a) Low gas flowrate
Figure 34: Photographs of Bubble Plume Shapes
156
Flow visualization at a water flow rate of 6.6 L/min and a gas flow rate of 2.0
L/min is shown in Figure 3. The individual frames show the progress of the dye at 30 s,
1 min, 1 min 30 s and 2min after the start of dye injection. Digital image processing was
used to remove variations in image color caused by uneven illumination. The black mark
seen at approximately one third the reactor’s height is the glass manufacturer’s mark.
As with salt tracer studies, in flow visualization studies the reactor was operated
at steady state for 4 theoretical hydraulic residence times prior to the introduction of the
non-reactive dye (dilute solution of buffered sodium indigo trisulfonate) to the reactor.
The dye was fed at a steady rate and concentration for 4 theoretical hydraulic residence
times. The color (darkness) of the image is proportional to the concentration of the dye.
The linear relationship between image color and dye concentration was ascertained
through analysis of digital images of the reactor filled with uniform solution of dye at 7
dilutions as described in section 0.
157
(a) 30 s (b) 1 min (c) 1 min 30 s (d) 2 min
Figure 35: Flow Visualization – Dye Progress at 30s, 1 min, 1 min 30s and 2 min(the Dark Triangle Approximately 1/3 the Reactor Height in Each Image is the
Glass Maker’s Manufacturer’s Mark)
The liquid phase does not exhibit plug flow behavior; dye proceeds unevenly in
the column, tending to flow faster near the column wall. Preferential flow of the dye near
the column wall is seen in frames (a) – (c). As the dye plume proceeds down the column,
158
dye is entrained into the bubble plume (in the center of the column) and back-mixes with
the down-flowing stream. This is seen in Figure 35(d). In that frame the front of the dye
plume is better mixed than in the prior 3 frames. Based on these observations, one can
expect early tracer breakthrough (due to the rapid progress of the dye near the column
wall), and a long tail on the residence time distribution arising from back-mixing of the
tracer into the bubble plume.
V.2 Residence Time Distribution Analysis
Experimental “F” curves corresponding to a liquid flow rate of 6.6 L/min and gas
flow rates ranging from 0 to 3 L/min are presented in Figure 36. The parameters and F
are the normalized time (t / tH) and the normalized concentration, defined above in
equation 37.
The early portions of the F curves in Figure 36 indicate that increased gas flow
rates promote earlier breakthrough. This is due, in part, to upward flow of liquid phase in
the bubble plume (“gulfstreaming”) and reduction of the effective column cross sectional
area through which downward-flowing liquid passes. Because the late portions of the F
curves approach the value 1.0 very slowly, it is clear there is significant hold-back or
back-mixing of the tracer in the reactor. This is likely due to entrainment of the tracer
into the bubble plume and transport of the tracer upward in the reactor.
159
0.0
0.2
0.4
0.6
0.8
1.0
0.0 0.5 1.0 1.5 2.0
F
No gas flow
Q = 0.5 lpm
Q = 1 lpm
Q = 2 lpm
Q = 3 lpm
Earlybreakthrough
Figure 36: Experimental Residence Time Distributions (RTDs) for 0 < Qg < 3 L/min
As described above, nonlinear regression was used to fit candidate residence time
distribution models to the experimentally measured residence distribution curves. The
gamma function (an approximation to the solution of the transient N-CSTRs in series
model) and the inverse Gaussian function (an approximation to the solution of the axial
dispersion model) were fit to the data by varying their model parameters. Since both
models have two parameters, the best fit model was the model yielding the lowest sum of
squares of errors between the model prediction and the experimental data. For all gas
160
flow rates the inverse Gaussian model provided the best fit to experimental data.
Peclet number, in environmental engineering applications, is defined in equation 53
(repeated below) (Weber 2001)
L
Ltcee
E
HUSRP ,
where Re is Reynolds number, Sc,t is turbulent Schmidt number, UL is liquid phase
superficial velocity, H is reactor height and EL is turbulent dispersion. Peclet number was
calculated from the variance of the inverse Gaussian distribution fitted to the tracer data
using equation 4 (repeated below)
eP
eeePP 122 21 (60)
where v is the dimensionless variance ratio.
Experimental relations found in the literature for Peclet number in countercurrent
bubble columns are presented in Table 20. With the exception of that of Baird and Rice,
all the relations presented in Table 20 were developed based residence time distribution
analysis of tracer. Baird and Rice developed their relation using analysis of images
captured on video cassette. In their work, they followed the mixing of two solutions of
different pH by tracking the front of a pH sensitive dye.
161
Table 20: Countercurrent Flow Peclet Number Relations
Relation Study
b
cg
Lv
duE
2
Bischoff and Phillips (1966)a
23.0 0.3G b c
e
L
u v dP
E
Reith et al. (1968)b
1 3 4 30.35
Ge
G C
u HP
u g d
Baird and Rice (1975)c
7 61 2
1
5 3
4.880.00185 9.7 G L
e
L b
uP
H u d
(Kim et al., 2002a)d
a Based on analysis of data from numerous small diameter cocorruent, countercurrent and nonflowingliquid phase bubble columns. Only valid in the ideal bubbly flow regime.b Based on experimental data taken in 5 cm and 14 cm cocurrent and countercurrent bubble columns inwhich air was sparged into tap water. The term 2ug + vb is the relative velocity between phases.c Developed using dispersion data collected from several studies and under the assumption of isotropicturbulence and turbulent energy dissipation rate equal to (ug g).d Developed for co- and countercurrent flow in a 15 cm circular bubble column. Units of H is in m and allother units must be dimensionally consistent.
162
0.1
1.0
10.0
100.0
1000.0
0 0.5 1 1.5 2 2.5 3 3.5 4
Gas Flow Rate (L/min)
Pec
let
Nu
mb
er
Reith
Kim
Baird
Experimental
CFD
Figure 37: Experimental and Predicted Peclet Number
Figure 37 shows Peclet number calculated from experimental data (as described
above) plotted along with Peclet number estimates from relations for countercurrent
bubble column Peclet number found in the literature and with estimates made using CFD
calculations. The experimental estimates of Peclet number are shown with a 90%
confidence interval. To estimate Peclet number from CFD calculations, the volume
averaged specific turbulence energy dissipation rate, , was calculated for each gas flow
rate and used in the expression proposed by Baird and Rice (1975) to calculate axial
163
dispersion
313435.0 cL dE (62)
The corresponding Peclet number was calculated using equation 53. Note that although
the parameter EL is usually called “axially dispersion” in environmental and chemical
engineering literature, the dispersion in the reactor is not uniform in the axial direction
and the term EL would be more aptly referred to as the average turbulent dispersion.
Peclet number falls sharply as gas flow increases from 0 to 0.5 L/min, is relatively
constant (around 3.0) for moderate gas flow rate and falls as gas flow rate increases
above 2 L/min. The Kim expression (listed in Table 20) fits experimental data well at
low and high gas flow rates. Reith estimate (listed in Table 20) fits the data at moderate
gas flow rate. Baird and Rice’s approximation to equation 31 ( cG dU ) consistently
underpredicts Peclet number.
CFD estimates for Peclet number offer the best match to experimental data,
falling within a 90% confidence interval around experimental values at intermediate gas
flow rates. Like experimental values, CFD estimate of Peclet number does not vary
significantly at intermediate gas flow rates. This agreement indicates that the CFD model
accounts for the important hydrodynamics in this regime.
Summarizing experimental observations, RTD analyses indicate three flow regimes
encountered over the range of gas flows. At low gas flow rate (1 L/min and below) there
is very little backmixing and the Peclet number falls sharply with increasing gas flow
164
rate. At intermediate gas flow rates (1.5 L/min ≤ Qgas≤ 2.5 L/min), the Peclet number is
relatively constant. In this regime the bubble plume rises asymmetrically in the column
and rotates as a function of time near the sparger. At high gas flow rates Peclet number
falls slightly and backmixing increases significantly. Churn turbulent behaviour
(significant bubble break-up and coalescence) was not observed during any experiment.
V.3 Numerical Studies
Numerical studies were performed to develop a detailed understanding of the
mixing phenomena and trends identified in experimental studies. Specifically, details
were sought on the variation in mixing over the axial extent of the reactor. Transient
simulations, summarized in Table 19, were performed at a liquid flow rate of 6.6 L/min
and gas flow rates ranging from 0.4 to 2.0 L/min. These cases were used to estimate
Peclet number (shown in Figure 37) and to generate velocity vector diagrams for
exploration of the changes in flowfield that occur with increasing gas flow rate.
A “virtual tracer study” was also performed in which the step feed and passage of
a conservative tracer through the reactor was simulated. Gas and liquid flow rates for the
virtual tracer study were 2.0 L/min and 6.6 L/min, respectively. Figure 38 shows
contours of virtual tracer concentration at 20, 40 and 60 s after introduction of the tracer.
Red indicates the tracer concentration is equal to the feed concentration and blue
indicates zero tracer concentration. The images in Figure 38 compare favorably with the
experimental flow visualization images found in Figure 35. As seen in experiments, the
CFD model predicts that the tracer projects downward into the reactor along the reactor
165
sides, swirling as it progresses.
Figure 38: Virtual Tracer Concentration at 20s, 40s and 60s after Step Input
Contours of gas volume fraction, g, predicted at a gas flow rate of 2 L/min are
shown in Figure 39(a). The plume does not rise symmetrically, but migrates in the
column and finally migrates to the wall near the top of the column. The plume region,
shown in Figure 39 (b) is defined as the region within which the liquid phase velocity is
166
upward. The surface shown in Figure 39 (b) is an isosurface where liquid vertical
velocity, wL, is equal to zero. Note that there is upflow of liquid in the bubble plume over
the entire reactor height and that the plume twists as it rises in the column. These figures
illustrate non-axisymmetric plume rise and significantly different plume shape near the
sparger compared with higher locations. In drinking water treatment, non-asymmetric
flow as illustrated in Figure 39 creates the potential for short-circuiting of raw water and
retards ozone mass transfer via poor mixing in the bubble plume and reduced contact of
bubbles with raw water. The uneven distribution of the phases seen in Figure 39 provide
an explanation for the great difference prior researchers have noted in Peclet number for
perfectly vertical columns and slightly tilted columns. The slight column misalignment
introduced into CFD calculations causes the bubble plume to migrate toward the wall and
contributes to the non-uniform distribution of phases.
167
0
0.01
0.02
0.03
0.04
0.05
g
(a) Gas volume fraction (b) Plume shape
Figure 39: Phase Distribution
Liquid superficial velocity vectors in the near-sparger region (the bottom 75 cm of
the reactor) at 4 gas flow rates are shown in Figure 40. At low gas flow rate (QG = 0.4
L/min) large recirculation regions appear on alternate sides of the plume, causing the
plume to rise in a wavy path. When gas flow rate is increased to 1.0 L/min, the bubble
plume diameter increases, squeezing the recirculation regions and resulting in faster
168
down-flow of liquid near the column wall. Increasing gas flow rate to 1.5 L/min further
increases the velocity of the down-flowing liquid near the column wall. At a gas flow
rate of 2.0 L/min, distinct recirculating regions similar to those seen at a gas flow rate of
0.5 L/min appear, though somewhat smaller and with greater rotational speed.
(a) QG = 0.4 L/min (b) QG = 1.0 L/min (c) QG = 1.5 L/min (d) QG = 2.0 L/min
Figure 40: Water Velocity Vectors near the Diffuser
The recirculating regions seen in Figure 40 explain the asymmetric plume rise
observed during laboratory experiments – these large structures, once established, deflect
the bubble plume. These recirculation regions differ from those typically found in bubble
column reactors with non-flowing liquid phase. In countercurrent flow, the large scale
169
flow structures move downward with the liquid flow, tending to swirl around the reactor
as they proceed. As these fluid structures progress, the bubble plume is deflected,
resulting in a chaotic bubble plume motion. The shapes and locations of large fluid
structures are strongly dependent on reactor geometry and the interaction between
downflowing liquid and bubble plume is also expected to be influenced by reactor
geometry. The boundary between the bubble plume and down-flowing liquid and the
preferential flow path for liquid are clearly seen in Figure 40. This segregation between
the phases is an impediment to mass transfer and provides a “Short-circuit” by which
some of the liquid phase passes quickly out of the reactor. In disinfection, this short
circuiting provides a path for pathogenic organisms to elude treatment.
Axial variation in mixing in the column is shown in Figure 41. Neglecting large-
scale fluid motion, local mixing intensity is approximately proportional to the square root
of the rate of turbulent energy dissipation (Droste 1997). Figure 41(a) shows contours of
turbulent kinetic energy dissipation on a column midplane and Figure 41(b) is a plot of
mean dissipation as a function of axial location. Average turbulent dissipation, kP , at
axial location k, is calculated by:
1 ,,g
elemnts#
1 ,,,g
i kiki
i kikiki
kA
APP
(63)
where Ai,k is area of element i at axial location k. Mixing is non-uniform both axially and
radially. Mixing is highest near the sparger (z < 0.5 m) and uniform in the rest of the
column, except near the top where entrance effects dominate the flow. Mixing intensity is
170
high inside the bubble plume; poorly mixed regions are observed outside the bubble
plume. These results provide an explanation for early breakthrough of tracer at high gas
flow rates (seen in Figure 36) – the flow field is partitioned into a well-mixed portion
rising in the bubble plume and a poorly mixed stream flowing downward.
Figure 41: Spatial Variations in Mixing
171
The observed variations in mixing along the axial extent of the reactor have mass
transfer implications. Near the sparger, though mixing in the bubble plume is intense,
liquid is rising in the bubble plume and has relatively high dissolved gas concentration;
the concentration gradient is low and mass transfer rate is low, despite intense mixing.
Away from the sparger mixing is uniform and the bubble plume is distributed more
evenly in the column. Based on these observations, local mass transfer rate near the
sparger is expected to be different from that away from the sparger. Currently, most
bubble column designs are based on an assumption that mass transfer is relatively
uniform in the reactor.
V.4 Influences of Inlet and Discharge Configurations
Most often in industrial and pilot scale ozone bubble contactors, liquid does not
enter the reactor opposing gas flow. Rather, it flows into the pilot reactor or chamber of a
full scale reactor perpendicular to the gas rise direction, as illustrated in Figure 42, a
schematic diagram of a full-scale ozonation reactor in current use in the Netherlands
(Smeets et al., 2006). Inlet hydrodynamics can exert a strong influence on the behavior
of the bubble plume(s) and the degree of mixing in the reactor. For example, for the
configuration shown in Figure 42, the cross-flowing water entering the dissolution
chamber is expected to deflect the bubble plume top toward the baffle wall and to
generate a large circulation in the dissolution chamber.
The impact of inlet and discharge configuration on the flow field in a
countercurrent flow bubble column was investigated via CFD modeling of a pilot scale
172
ozone bubble column reactor operated by the Philadelphia Water Department (Charlton
2003). The Philadelphia Water Department evaluated ozone disinfection as an alternative
to chlorine for improved inactivation of Cryptosporidium parvum and reduced formation
of disinfection by-products (DBPs). The pilot study indicated that bromide
concentrations observed in Schuylkill River water gave rise to unacceptable bromate
concentrations when treated with ozone and alternative means for DBP control were
adopted.
Figure 42: Typical Intake Configuration for Countercurrent Full Scale Ozonation
173
V.4.1 Philadelphia Water Department Pilot Disinfection Unit
The PWD pilot disinfection operation was comprised of 9 right circular
cylindrical reactors, each 15.2 cm (6 inches) in diameter arranged in series. Each column
was plumbed to allow operation in either cocurrent or countercurrent mode. Air or
ozonated air could be introduced into any of the first 4 columns in the pilot plant. Air or
ozonated air was sparged into the bottom of bubbled columns via a distributor plate.
Flow entered and was discharged from the columns via 6.4 cm (2.5 in) pipes, as seen in
Figure 43. In Co-current flow mode, the water entered the column perpendicular to the
column centerline approximately 10 cm above the sparger and exited the column
approximately 10 cm below the water surface. In countercurrent flow, the water entered
the reactor at the top and exited at the bottom.
Results of CFD analysis of the PWD pilot reactor are presented in Figure 43 -
Figure 45. In Figure 43, color contour plots of the gas volume fraction are shown for a
plane that passes through the reactor centerline. The water and gas flow rates for this
simulation were 37 L/min and 3.5 L/min. The CFD model of the first bubble column in
the PWD pilot reactor employed a mesh of 208,044 tetrahedral elements, with mesh
clustering near the intake and discharge ports, uniform bubble diameter of 2 mm and
specified medium turbulence intensity at the reactor water intake. All other model
components were the same as those described for the laboratory reactor model.
The inlet and discharge configurations result in deflection of the bubble plume
toward the discharge (at the reactor bottom) and away from the intake (at the top of the
174
reactor). At the intake and discharge the distribution of phases is much less uniform than
in the middle of the reactor. This poor distribution of phases results in lower mass
transfer than is the phases were more evenly distributed, despite relatively energetic gas
phase. Velocity vectors showing superficial liquid velocity near the reactor intake and
discharge are plotted in Figure 44. A large vortex is present in the reactor in the portion
of the reactor opposite the discharge port. This vortex results in significant back-mixing
of the liquid phase and high dispersion, even though the phases are poorly distributed.
The water intake configuration promotes a strong flow of liquid along the column wall
directly opposite the intake.
Results of a virtual tracer study of the PWD pilot reactor operated in
countercurrent mode are presented in Figure 45. As expected based on the velocity
vectors plotted in Figure 44, the tracer flows quickly down the reactor wall opposite the
intake and discharge side until the tracer front reaches the large vortex in the bottom of
the reactor. In the bottom of the reactor, the vigorous back-mixing results in a region of
uniform tracer concentration, despite poor distribution of phases.
The importance of inlet and discharge configuration in determining the residence
time distribution and hydrodynamics of bubble column contactors is not unique to tall,
cylindrical columns such as those used by the Philadelphia Water Department – Ta and
Hague (2004) found that inlet and discharge configurations were the dominant factor in
the flow field for a right rectangular cylindrical bubble contactor with the inlet transverse
to the flow direction and with a much lower aspect ratio than the Philadelphia Water
175
Department contactor. Since full scale reactors typically employ inlets and discharges
perpendicular to the flow direction, care should be taken in accounting for inlet and
discharge hydrodynamics in scaling from pilot to full scale.
Figure 43: Philadelphia Water Department Pilot Column Phase Distribution
176
(a) Reactor Discharge Region (a) Reactor Intake Region
Figure 44: PWD Pilot Reactor Intake and Discharge Region Velocity Vectors
177
NormalizedTracer
Concentration
Figure 45: PWD Virtual Tracer Study
178
VI MASS TRANSFER STUDIES
Flow visualization and computational fluid dynamic studies were performed of
mass transfer in the laboratory bubble column reactor. These studies allowed
quantification of spatial variations in mass transfer in a simple cylindrical bubble column
reactor. The studies also demonstrated that, without a priori knowledge of mass transfer
coefficient and without calibration, a computational fluid dynamic model can be used to
predict phase distribution and mass transfer in countercurrent bubble column flow. Thus
CFD should be considered more reliable than currently-used models for scale-up of
bubble column reactors from pilot scale to full scale.
In this chapter, results from the ozone mass transfer visualization technique
described above are presented and a qualitative description of countercurrent
hydrodynamics and mass transfer in a cylindrical column is provided. Processed images
of indigo dye are then used for estimation of mass transfer rate, dispersion and entrance
region length for the bubble column operating at three liquid flow rates and two gas flow
rates. Images of indigo dye are compared with images generated using CFD and CFD is
compared to other countercurrent flow models. Finally, the impact of choice of mass
transfer submodel in a CFD model is quantified.
VI.1 Matrix of Mass Transfer Studies
Mass transfer visualization experiments were conducted at three gas flow rates
and three liquid flow rates. In all but one experiment, ozone generator voltage was
chosen to provide a wide variation in indigo dye concentration in the reactor while
179
ensuring the indigo was not decolored anywhere in the reactor. In the single experiment
conducted at the highest gas flow rate, the indigo dye was decolored above the bottom of
the reactor. Though the images taken of that case could not be used in the estimation of
mass transfer rate or mixing, they did allow visualization of entrainment of indigo dye
into the bubble plume.
The mass transfer visualization experiments conducted are summarized in Table
21. Experiments run at the same gas and liquid flow rates are designated case A and case
B. The range of gas to liquid flow ratios used in experiments are typical of those used in
prior pilot studies and in full scale facilities (Mariñas et al., 1993; Owens et al., 2000).
Table 21: Mass Transfer Visualization Experiments
Tap waterflow rate(lpm)
Indigostock flowrate (lpm)
Net liquidflow rate,QL (lpm)
Gas flowrate, QG,(slpm) QG / QL Case
Ozonegeneratorvoltage
Discharge watertemperature (°C)
6 1 7 0.4 0.057 A 60 22
6 1 7 0.4 0.057 B 65 16
9 1.5 10.5 0.4 0.038 A 60 20
9 1.5 10.5 0.4 0.038 B 65 12
12 1.5 13.5 0.4 0.030 A 65 9
12 1.5 13.5 0.4 0.030 B 70 4.5
6 1 7 0.7 0.100 65 17
9 1.5 10.5 0.7 0.067 65 20
12 1.5 13.5 0.7 0.052 70 20
9 1.5 10.5 0.9 0.087 70 22
180
VI.2 Ozone Mass Transfer Visualization Results
The indigo dye ozone mass transfer visualization technique allowed qualitative
and quantitative observations of the mass transfer process. In this section, images from
the mass transfer visualization technique are presented and the hydrodynamics of mass
transfer are described. Next, estimates of Peclet number and Stanton number are made
using radially-averaged indigo dye color data and the variation in these parameters with
column gas to liquid flow ratio is documented.
VI.2.1 Observations
The indigo dye mass transfer visualization technique yielded vivid images that
allowed direct observation of mixing and mass transfer in the laboratory reactor. As
described above, the influent indigo dye concentration and gas phase ozone concentration
were chosen to provide the widest possible variation in indigo dye color between the
reactor top and bottom but to ensure indigo dye was present in the reactor discharge.
Images showing indigo dye decoloration at gas to liquid flow rates of 0.06 and
0.03 are presented in Figure 46. The only processing performed on the two images in
Figure 46 was elimination of background variations in lighting. The light triangular mark
approximately 1/3 of the axial distance between the reactor bottom and top is the
manufacturer’s mark (physically present on the laboratory reactor wall). The sparger and
glass bead packing appear white in the images because there was no difference in color
between the indigo dye image and the background image from which it was subtracted.
181
(a) Qg/QL= 0.06 (b) Qg/QL= 0.03
Figure 46: Indigo Dye Decoloration Images
182
Both of the images shown in Figure 46 were taken while ozone was being fed to
the reactor and after the reactor reached quasi-steady state (as described in Chapter III).
Image (a) was taken at gas and liquid flow rates of 0.4 slpm and 7.0 lpm (gas to liquid
flow rate of 0.06), ozone generator voltage of 65 V and indigo dye inlet concentration of
5.5 mg/L. Image (b) was taken at gas and liquid flow rates of 0.4 slpm and 13.5 lpm (gas
to liquid flow ratio of 0.03), ozone generator voltage of 65 V and indigo dye inlet
concentration of 4.3 mg/L.
There are significant differences in the pattern of indigo dye decoloration
observed in Figure 46 (a) and Figure 46 (b). At high gas to liquid flow rate (Figure 46
(a)), there is a relatively sharp decline in indigo dye concentration near the top of the
reactor. Asymmetric flow of the indigo dye downward can be observed at the top of the
reactor and slightly below the manufacturer’s mark. Large swirls of dye (length scale on
the order of the column diameter) are observed throughout the reactor, particularly in the
bottom half of the reactor. At high gas-to-liquid flow ratios, in the bottom half of the
reactor, dye projected downward along the column wall and large eddies of dye-rich
liquid were entrained into the bubble plume, decoloring rapidly after entrainment. At a
low gas to liquid flow ratio (Figure 46 (b)), the decoloration of indigo dye is more
uniform in the liquid flow direction than at the high gas to liquid flow ratio.
In both images, the concentration of indigo dye appears to increase at the very
bottom of the reactor. This increase is more pronounced in the high gas-to-liquid flow
ratio and was observed in most of the images obtained during mass transfer visualization
183
experiments. It is hypothesized that this increase is a result of the entrainment of indigo
dye-rich liquid outside the bubble plume into the large recirculating regions near the
sparger shown in Figure 40.
The progress of dye-rich eddies downward is shown more clearly in Figure 47. In
that figure, images 1 and 2 were both taken at quasi-steady state, approximately 20
seconds apart. Images were converted to grayscale and contrast was enhanced to
accentuate the indigo dye color. For the images in Figure 47, gas and liquid flow rates
were 0.9 slpm and 10.5 lpm, respectively, the ozone generator was operated at a voltage
of 70 V, and indigo dye intake concentration was 5.5 mg/L. These operating conditions
resulted in near complete discolorization of the indigo dye upstream of the discharge.
Complete discolorization produced images that show flow details very well.
Large eddies with high indigo dye concentration and with length scale on the
order of column diameter appear to flow downward outside the bubble plume core,
spiraling around the reactor as they proceed. As they descend these eddies are entrained
into the bubble plume and decolored rapidly. The images in Figure 47 indicate two
important mixing length scales: mass transfer from bubbles to liquid depends upon
mixing on the length scale of the order of the bubble diameter. Transport of “fresh”
liquid to the bubble plume from the bulk liquid phase depends on mixing on the length
scale of the column diameter. Figure 47 also indicates that even within the dispersed
bubble flow regime, discharge indigo dye concentration is unsteady, because the
transport of the large indigo-rich eddies is a time dependent random process. This
184
observation is constituent with measurements of effluent ozone concentration in full-scale
ozone fine bubble contactors (Schulz and Bellamy 2000) and should be considered when
evaluating sample ozone residual concentration data for making Ct estimates.
(a) Image 1 (b) Image 2
Figure 47: Eddy Transport during Ozonation
185
VI.2.2 Parameter Estimates
Images from mass transfer visualization studies were used to estimate mass
transfer rate and dispersion. The steps in this process were:
Processing of indigo dye images (subtraction of background and conversion to
greyscale);
Calculating radially averaged indigo dye concentration data from processed indigo
dye images;
Application of non-linear regression to determine the parameters of candidate models
for the fate and transport of indigo dye that produce the best fit of data from indigo
dye images; and
Comparison of fitted models to determine the model that best fit the data.
VI.2.2.1 One-Dimensional Indigo Dye Decoloration Models
As described above and observed by prior researchers (Rice and Littlefield 1987;
LeSauze et al., 1993), in the top portion of the laboratory reactor, indigo dye was
decolored more or less monotonically as the dye flowed downward. Near the sparger,
however, the dye concentration was nearly uniform, exception where large eddies of dye-
rich water flowing near the walls were entrained into the bubble plume. This tendency is
illustrated in Figure 48, which shows an image of indigo dye concentration along with a
plot of radially-averaged indigo dye concentration.
186
0.4 0.5 0.6 0.7 0.8 0.9 1.0
1.0
0.8
0.6
0.4
0.2
Well-mixedzone
z*
CI*
Figure 48: Illustration of Well-Mixed Zone and Radially-Averaged Concentration
The gas and liquid flow rates corresponding to Figure 48 were 0.4 slpm and 13.5
lpm, respectively. The terms z* and CI* are nondimensional depth and dimensionless
indigo dye concentration, given by
H
zz * (64)
and
187
0,
*
I
II
C
CC (65)
where z is depth from the water free surface, H is reactor height (from the
discharge ports to the water free surface), CI is indigo dye mass concentration and CI,0 is
indigo dye concentration at the liquid inlet.
Based on this observation, two models for indigo dye decoloration were proposed:
a single-zone model in which the dispersion and mass transfer coefficient were
assumed uniform in the reactor and
a two-zone model in which the portion of the reactor near the sparger was modeled as
a continuously stirred tank reactor (CSTR) and the rest of the reactor was modeled
using the 1-dimensional advection-dispersion-reaction (ADR) model.
Detailed derivation of expressions for indigo dye concentration for the one- and
two-zone models are provided in Appendix B and summarized below.
For the single-zone model, normalized indigo dye concentration is given by
**
111* zPPS
zSNSNe
eS
IeeSS eeSNeeP
PSNC
(66)
where NS is Stanton number, given by
;L
LS
U
HakN (67)
188
S is stripping factor, given by
;L
G
U
UmS (68)
Pe is Peclet number, defined in equation 39 (repeated below)
D
HUP L
e (39)
and the parameter is given by
0,
0
0,
0 3
3
3
3 I
gO
L
G
O
I
I
gO
O
I
C
C
Q
Qm
M
MS
C
C
M
M (69)
In equations 37, 59 - 61, kL is liquid side mass transfer coefficient, a is specific surface
area, m is Henry’s law constant (dimensionless ratio of mass concentration in gas phase
to mass concentration in liquid phase), UG and UL are superficial gas and liquid flow
rates, MI and3OM are molecular weights of potassium indigo trisulfonate and ozone,
03 gOC is gas ozone concentration at the sparger, and CI,0 is indigo trisulfonate
concentration at the water intake. Measured water temperature ranged from 4.9° C to 22°
C over the course of mass transfer visualization experiments and Henry’s law constant
was calculated via the expression (Perry and Chilton 1973)
C5C51687
2.6
C5C5840
25.3log
TT
TTm (70)
189
In the limit of NS Pe, the single zone expression for normalized indigo dye
concentration becomes
e
PzPee
I PeezPPC
ee
ePS
SN
111*
lim
1*
*
(71)
Two versions of the two-zone model were fit to experimental data. In one version
the Stanton number was assumed the same in zones 1 and 2 and only mixing differed
between the two zones. The indigo dye concentration for this model is given by
****
**
*
*2,
*
11
1
1
cSecS
ee
zSNzPzzSN
cSeS
e
zPI
zPI
eezSNPSN
P
eCeC
(72)
where Pe refers to the Peclet number in zone 1 (the top of the reactor), zc* is the
nondimensionalized critical depth and *2,IC is the dimensionless indigo dye concentration
in zone 2 (the well mixed zone) given by
data
c
n
niiI
cdataI
I CnnC
C ,
0,
*2,
11(73)
where ndata is the number of (pixels) in the indigo dye image and nc is the row
corresponding to the critical depth.
For the two-zone model in which different Stanton numbers were allowed in
zones 1 and 2, the expression for indigo dye concentration is
190
*
1***
1
**
*21
*2,
*
11
1
1
cSecS
ee
zSNzPzzSN
cSeS
e
zPI
zPI
eezSNPSN
P
eCeC
(74)
where NS1 and NS2 are the zone 1 and zone 2 Stanton numbers. In the limit eS PSN 1 ,
the expression for indigo dye concentration becomes
*2
**
2,*
111
**
**
cS
zzPezP
IzP
IzSN
ezPeCeC
ce
ee
(75)
VI.2.2.2 Methodology for Determining Model Parameters
Model equations 58, 62, 65 and 66 were fit to radially-averaged indigo dye
concentration data from digital photographs of mass transfer visualization experiments.
Fits were made using the nls (nonlinear least squares) utility in the R programming
language (The R Foundation 2006). After models were fit to data, independence was
assessed via runs tests (Manly 1997). Data were considered independent unless
independence could be rejected with 95% confidence.
When dependency was encountered, a subset of data was taken from the original
data set, best fit parameters were again determined and independence was again assessed.
Two sampling methodologies were assessed when selecting subsets from the original
data set. In one, a random sample of ndata/j points was taken from the original data set,
where ndata was the number of data points (rows) in the original data set and j took the
values 2, 4, 8, 16, 20, 24, 28, 32, 36, 40, 44, 48, 52, 56, 60 and 64. In the second
191
sampling methodology a systematic sample was taken in which the subset consisted of
each jth data point where j took the values 2, 4, 8, 16, 20, 24, 28, 32, 36, 40, 44, 48, 52,
56, 60 and 64. In all cases the systematic sampling resulted in elimination of dependence
at lower values of j than the random sampling. Reducing the number of data points did
not result in significant changes in parameter estimates. In all cases, independence could
be demonstrated for the two-zone model (usually after the number of data points in the
sample was 20 times less than that in the original data set). Independence could not be
demonstrated for any cases for the single-zone model. Thus, the two zone model was
considered the more appropriate model and parameter estimates were taken from the two-
zone model.
In two zone models, the critical depth, zc*, was determined as follows. The best
fit parameters and sum of the squares of the errors were determined for all zc* (0.5,
1.0). The critical depth was taken to be the value that gave the lowest sum of squares of
errors. The minimum sum of the squares of the errors was usually readily identifiable. A
typical plot of sum of the squares as a function of index of critical depth is provided in
Figure 49. In digital images, each row of pixels corresponds to a value of z*, so in Figure
49, the index nc is the row number corresponding to the critical depth zc. For the plot
shown, there was a total of 60 data points and the critical depth was determined to be at
the 44th data point.
An R-language script used for determination of two-zone model best fit
parameters and for performing a runs test of the fitted model is provided in Appendix D:
192
Similar scripts were written for the one zone model and for versions of the models in
which the Peclet and Stanton numbers were equal.
30 35 40 45 50 55 60
0.0
02
20
.002
40
.002
60.0
028
nc
SS
E
Figure 49: Identification of Best Fit Critical Depth
VI.2.2.3 Parameter Estimates
Processed images, best-fit models and parameters corresponding to best fit
models for each mass transfer visualization experiment are presented below. For each of
the indigo dye experiments, two images and plots showing 1- and 2-zone best fit models
are shown in Figure 51 - Figure 59. Both color (blue) and grayscale images are provided,
193
since the color images provide greater detail in the variation of indigo dye color. Along
with reactor images, plots of best fit 1-zone and 2-zone models are provided. In all cases,
independence could not be demonstrated for the one-zone model; the one-zone plots are
included in Figure 51 - Figure 59 for contrast with best fits of the two-zone model and to
document the trends in data that gave rise to data dependence. Data dependence is
manifested in either periodic variation of the data around the model (such as seen in
Figure 53 (c)) or significant deviation of the model from the data at the top and bottom of
the reactor (such as seen in Figure 52 (c)).
Several general observations can be made based on Figure 51 - Figure 59. First,
in all cases, in the top of the reactor the indigo dye concentration decreases steadily as the
water progresses downward. Second, the rate of decrease of indigo dye in the bottom of
the reactor is always less than that in the top of the reactor (though not necessarily zero,
as would be observed in a true CSTR). Third, in several cases (Figure 53, Figure 56,
Figure 58 and Figure 59) there is an upturn in indigo dye concentration at the very bottom
of the reactor. One explanation for this upturn is that dye-rich water flowing along the
column walls is backmixed into the column as the water is entrained into the large eddies
near the sparger (as seen in Figure 40). As seen later in this chapter, CFD also predicts
there is a region of high indigo concentration at and below the sparger depth. Finally, the
inability to demonstrate independence for the single zone model is related to large length
scale oscillations in indigo dye concentration around the trend line. These oscillations are
not surprising, given the observation of large dye-rich eddies flowing downward in the
194
reactor, and indicate that time series analysis of radially-averaged indigo dye
concentration data might yield quantitative data on large scale mixing processes.
195
Figure 50: Mass Transfer Visualization, Qgas = 0.4 slpm, QL = 7.0 lpm, Case A
196
Figure 52: Mass Transfer Visualization, Qgas = 0.4 slpm, QL = 7.0 lpm, Case B
197
Figure 53: Mass Transfer Visualization, Qgas = 0.4 slpm, QL = 10.5 lpm, Case A
198
Figure 54: Mass Transfer Visualization, Qgas = 0.4 slpm, QL = 10.5 lpm, Case B
199
Figure 55: Mass Transfer Visualization, Qgas = 0.4 slpm, QL = 13.5 lpm, Case A
200
Figure 56: Mass Transfer Visualization, Qgas = 0.4 slpm, QL = 13.5 lpm, Case B
201
Figure 57: Mass Transfer Visualization, Qgas = 0.7 slpm, QL = 7.0 lpm
202
Figure 58: Mass Transfer Visualization, Qgas = 0.7 slpm, QL = 10.5 lpm
203
Figure 59: Mass Transfer Visualization, Qgas = 0.7 slpm, QL = 13.5 lpm
204
Best fit parameters for each mass transfer visualization experiment are presented
in Table 22. In Table 22, the sample size at which independence could not be rejected
with 95% confidence was ndata / j where ndata is the number of data points in the full data
set. In general, Peclet number estimates were found to vary more widely than estimates
for Stanton number and length of the entrance region. In one case (gas flow rate of 0.4
slpm, liquid flow rate rate of 10.5 lpm, case B) the zone 2 Stanton number was estimated
to be zero. This indicates that the change in indigo color observed in the top of the
reactor can be attributed solely to mixing and that all significant mass transfer takes place
in the well-mixed zone in the bottom of the reactor.
Table 22: Best Fit Parameters
Qg (slpm) QL (lpm) Case j Pe NS1 NS2 zc*
0.4 7.0 A 24 1.49 0.29 0.29 0.266
0.4 7.0 B 56 1.93 0.43 0.43 0.282
0.4 10.5 A 32 5.77 0.16 0.025 0.226
0.4 10.5 B 16 1.66 0.19 0.00 0.240
0.4 13.5 A 16 2.04 0.14 0.14 0.173
0.4 13.5 B 36 7.76 0.10 0.10 0.216
0.7 7.0 24 1.91 0.96 0.96 0.396
0.7 10.5 28 1.52 0.35 0.35 0.266
0.7 13.5 24 1.93 0.38 0.38 0.219
205
Peclet number, Stanton number and critical depth were found to correlate with the
ratio of gas to liquid flow rates. Figure 60 shows the variation in entrance region length
(1 - *cz ) with gas to liquid flow ratio. Estimates based on data from experiments
conducted at a gas flow rate of 0.4 slpm are shown as solid diamonds and those based on
experiments at a gas flow rate of 0.7 slpm are shown as unfilled squares. Entrance region
length increases steadily with increasing gas to liquid flow ratio for the gas and liquid
flow rates used in this study. This result indicates that high gas to liquid flow rates result
in greater mixing of the liquid phase (primarily through the formation of large vortices in
the vicinity of the sparger and attendant backmixing of the liquid phase) but less uniform
distribution of the phases. In a more complex reactor geometry than that of the
laboratory rector used in this study, uneven distribution of phases creates the potential for
short-circuiting of the liquid phase in the bubble column and could result in significant
variations in ozone residuals, as has been observed in full-scale ozonation reactors
(Schulz and Bellamy 2000).
206
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1 0.11
Gas to Liquid Volumetric Flow Ratio
En
tra
nce
reg
ion
len
gth
(%o
fre
act
or
hei
gh
t)
0.4 slpm
0.7 slpm
Figure 60: Variation of Entrance Region Length with Gas to Liquid Flow Ratio
As expected, zone 1 Stanton number increases with gas to liquid flow ratio, as
seen in Figure 61. Higher gas flow rates produce more bubbles, resulting in greater
dispersion (in the bubble wakes) and higher specific surface area (a). Had gas phase
holdup been measured during mass transfer visualization studies, the relative importance
of these two changes (increased dispersion and increased specific surface area) could
have been ascertained.
207
0
0.2
0.4
0.6
0.8
1
1.2
0 0.02 0.04 0.06 0.08 0.1 0.12
Gas to Liquid Volumetric Flow Ratio
Sta
nto
nN
um
ber
Figure 61: Variation of Zone 1 Stanton Number with Gas to Liquid Flow Ratio
The variation of zone 1 Peclet number with gas to liquid flow ratio is shown in
Figure 62. As noted in Table 22, there was wide variation in Peclet number estimates
from indigo dye image analysis, indicating high uncertainty in Peclet number estimates,
especially at low gas-liquid flow ratios. In general, data follow the trends in Peclet
number determined via RTD studies and CFD analyses shown in Figure 37, except for
one estimate of Peclet number at the lowest gas to liquid flow rate. Images and best fit
model for the case with the unexpectedly low Peclet number are found in Figure 56.
Images and best fit model for the other case at the lowest gas to liquid flow ratio are
208
found in Figure 55. The only difference in operating conditions between the two cases is
the ozone generator voltage: the voltage for the low Peclet number case was 70 V and
that for the other case was 65 V. Based on the images in Figure 56, it is possible that
some of the liquid phase was completely decolored for the case run at the higher ozone
generator voltage and this may have made the Peclet number estimate less accurate.
0
1
2
3
4
5
6
7
8
0 0.02 0.04 0.06 0.08 0.1 0.12
Ratio of Gas to Liquid Volumetric Flow Rate
Pec
let
Nu
mb
er
Figure 62: Variation of Zone 1 Peclet Number with Gas to Liquid Flow Ratio
The most significant findings and observations from the experimental mass
transfer studies are that:
The mass transfer and mixing near the sparger (in the “entrance region”) differ from
209
those in the rest of the reactor.
The entrance region length can be determined using the indigo dye mass transfer
visualization technique.
The entrance length increases with increasing gas to liquid flow ratio.
Although the entrance region liquid phase is well-mixed, distribution of phases in the
entrance region is poor.
Stanton number increases with increasing gas to liquid flow ratio, likely because of
specific surface area and turbulent dispersion increases.
Peclet number trend is similar to that measured in RTD studies and predicted in CFD
studies.
VI.3 CFD Mass Transfer Modeling Results
As described above, CFD was used to predict ozone mass transfer and fate and
transport of indigo dye. Recapping important CFD model features, bubbles were
assumed monodisperse with a diameter of 2.5 mm, bubble drag was estimated using the
Grace drag model (Clift et al., 1978), mass transfer rate was estimated using the Kawase
mass transfer relation (Kawase and Moo-Young 1992) and the indigo-ozone reaction was
assumed sufficiently fast that there was no accumulation of dissolved ozone. The CFD
model was run to allow comparison of predictions with results of four mass transfer
visualization experiments:
210
QG = 0.4 slpm, QL = 7.0 lpm, case A
QG = 0.4 slpm, QL = 13.5 lpm, case A
QG = 0.7 slpm, QL = 7.0 lpm, and
QG = 0.7 slpm, QL = 13.5 lpm.
Direct comparison was made between indigo dye concentrations predicted by
CFD and measured concentrations from samples drawn from the reactor. Samples were
drawn from the reactor centerline from regularly spaced sample ports on the laboratory
bubble column. The sample ports were sealed with Teflon seals held in place by fittings
that allowed samples to be drawn from the sample centerline by 25 cc glass syringes
outfitted with 3 inch (7.62 cm) hypodermic needles. Sample locations are shown in
Figure 63.
Prior to sampling, the reactor was run at steady water and gas flow rates and
ozone dose for more than three hydraulic residence times. Samples were drawn from one
sample port at a time, beginning with the top port and proceeding to the bottom.
Individual samples required up to 20 seconds to draw and the entire sampling process
took approximately 2 minutes. Sample sizes were small (between 11 and 15 cc).
Samples were diluted with enough milli-Q water to make the total sample volume 40 cc
(the minimum sample volume for the 1 inch diameter (2.5 cm) spectrophotometer cells
used) and absorbance was measured using a spectrophotometer. Absorbance of samples
was measured at 500 nm and indigo concentration was calculated for samples using the
211
calibration curve described in Chapter III and accounting for dilution.
Figure 63: Sample Locations
Sample and CFD normalized indigo dye concentrations are compared in Figure
64. CFD results agree very well with sample concentrations at the bottom and top of the
reactor, but are consistently lower in the center of the reactor. It is difficult to assess the
CFD model based on this comparison. As described above, flow in the reactor is
decidedly three dimensional and transient
212
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
z*
CI*
CFD
Experimental
Figure 64: Predicted and Measured Indigo Dye Concentrations
Color contours and grayscale contours from CFD analyses are presented next to
processed experimental indigo dye images in Figure 66 - Figure 69. Qualitatively, the
consumption of indigo dye in the CFD images is very close to that of the experimental
image. Differences in indigo dye concentration radial distribution between the
experimental and CFD are related to differences between how the CFD image and the
image captured on camera were generated. The experimental image is a two dimensional
213
image of the average indigo concentration at a particular location (r, z) on the image
background, as illustrated in Figure 65. The CFD image shows indigo contours at a plane
passing through the centerline of the reactor. Additionally, portions of bubble surfaces
appear as dark spots in the experimental image, making the bubble plume look slightly
darker than it should. As described in the experimental methods indigo dye concentration
calibration portion of this thesis (section III.3.4), the indigo dye calibration curve
(relating indigo dye concentration to image pixel color) was developed for images with
bubbles. In CFD images, no bubbles are present and this difference results in minor
differences between CFD and experimental images of indigo concentration.
Image
Image
(a) Image Location, Experimental Image (b) Image Location, CFD
Figure 65: Image Location, Experimental Images and CFD
214
The impact liquid flow rate has on spatial distribution of mass transfer can be seen
through comparison of Figure 66 and Figure 67. The gas flow rate was the same for both
cases (0.4 slpm) and the liquid flow rates are 7.0 lpm and 13.5 lpm, respectively. In the
high gas to liquid flow ratio case (Figure 66), indigo dye is decolored nearly to the top of
the reactor, with the lowest indigo concentration water found in the bubble plume slightly
above the sparger. At high liquid flow rate, the region in which indigo dye is decolored
is much shorter, reaching only the reactor mid-height. In the high liquid flow case, there
is vigorous backmixing of the liquid phase near the sparger and ozone is stripped from
the gas phase rapidly near the sparger as a result of this mixing. At a gas flow rate of 0.7
slpm, the trend of mass transfer occurring over a greater portion of the reactor at the low
liquid flow rate (Figure 68) than at high liquid flow rate (Figure 69) is again observed.
Comparing the CFD and experimental images, some of the flow structure
observed in the experimental images is not seen in the CFD images. For example, Figure
69, large swirls of high indigo dye concentration water are observed in the bottom half of
the reactor. The absence of these eddies in the CFD results is a result of the choice of
turbulence model. Had a LES (large eddy simulation) model been chosen instead of the
- implemented, these eddies might have been identified, though a finer mesh and
smaller time step would have been required.
215
(a) Experiment (b) CFD, Color Contours (c) CFD, Grayscale
*IC *
IC
Figure 66: Experimental and CFD Indigo Dye Image, QL = 7.0 lpm, QG = 0.4 slpm
216
(a) Experiment (b) CFD, Color Contours (c) CFD, Grayscale
*IC *
IC
Figure 67: Experimental and CFD Indigo Dye Image, QL = 13.5 lpm, QG = 0.4 slpm
217
(a) Experiment (b) CFD, Color Contours (c) CFD, Grayscale
*IC *
IC
Figure 68: Experimental and CFD Indigo Dye Image, QL = 7.0 lpm, QG = 0.7 slpm
218
Figure 69: Experimental and CFD Indigo Dye Image, QL = 13.5 lpm, QG = 0.7 slpm
(a) Experiment (b) CFD, Color Contours (c) CFD, Grayscale
*IC *
IC
219
To allow direct comparison of CFD predictions with data from mass transfer
visualization images, CFD predictions for indigo dye concentration were averaged on
horizontal planes (area-weighted averaging) and plotted along with radially-average
indigo dye data. The results of this comparison are plotted in Figure 70- Figure 73.
Figure 70 shows a plot of CFD and experimental average indigo dye concentrations
measured/calculated at a gas flow rate of 0.4 slpm and a liquid flow rate of 7.0 lpm. The
CFD model predicts the slope of the experimental indigo dye curve quite well, though the
CFD results are off-set from the experimental results. Figure 71 compares measured and
predicted indigo dye concentration at a gas flow rate of 0.4 slpm and a liquid flow rate of
13.5 lpm. Again, the CFD results have the same slope as the experimental results, but are
significantly off-set from the experimental values. Figure 72 compares measured and
predicted indigo dye concentration at a gas flow rate of 0.7 slpm and a liquid flow rate of
7.0 lpm. The CFD predictions are in worse agreement with experimental values at these
operating conditions than for any other cases, though the CFD model predicts the net
indigo dye consumption in the reactor fairly accurately. It appears the CFD model does
not adequately model the mixing zone near the sparger. Finally, Figure 73 compares
measured and predicted indigo dye concentration at a gas flow rate of 0.7 slpm and a
liquid flow rate of 13.5 lpm. Again, the CFD model predictions appear offset from the
experimental values.
One plausible explanation for the offset observed between observed and predicted
indigo dye concentrations is uncertainty in reactor influent indigo dye concentration.
220
Indigo dye solution was delivered to the influent plumbing via a peristaltic metering
pump. Prior to experiments, the pump was calibrated via measurement of water flow rate
and comparison with pump read-out. These measurements were made with the pump
discharging to atmospheric pressure through a short length of tubing. It is possible that,
with the pump delivering water to the column, the pump delivery rate differed from that
measured during calibration studies or that the pump delivery rate varied during
experiments due to chaffing of the tube through indigo dye solution was delivered.
Figure 70: Comparison of CFD and Experimental Indigo Dye Concentration Data,Q6=0.4 slpm, QL=7.0 lpm
221
Figure 71: Comparison of CFD and Experimental Indigo Dye Concentration Data,Q6=0.4 slpm, QL=13.5 lpm
222
Figure 72: Comparison of CFD and Experimental Indigo Dye Concentration Data,Q6=0.7 slpm, QL=7.0 lpm
223
Figure 73: Comparison of CFD and Experimental Indigo Dye Concentration Data,Q6=0.7 slpm, QL13.5 lpm
224
VII CRYPTOSPORIDIUM INACTIVATION AND BROMATE FORMATION INA FULL-SCALE REACTOR
A rough CFD model was developed to demonstrate CFD prediction of mass
transfer, Cryptopsoridium parvum inactivation, bromate formation and ozone decay in a
full scale reactor. Here, rough means 2-dimensional and with a relatively coarse mesh.
Because the intent of the full scale modeling effort was demonstration and not rigorous
prediction, the rough model was deemed adequate. Had more accurate results been
required, a more detailed CFD study would have been conducted more methodically and
would have included a mesh sensitivity analysis and validation with experimental data.
VII.1 Description of Full Scale Reactor
The full-scale reactor modeled in this demonstration is the Alameda County
Water District (ACWD) ozone contactor located in Fremont, CA. Design and operating
condition details for the reactor were drawn from the study by Tang et al. (2005). In that
study, the authors assessed the ability of the one-dimensional advection-dispersion-
reaction model (ADR) to predict Cryptosporidium parvum inactivation and bromate
formation in a full scale reactor. The authors determined that the ADR model, when
calibrated with dispersion data from tracer studies, provided “good” agreement with
experimental data (calculated v. predicted ozone residual, Cryptosporidium parvum
surrogate concentration and bromate concentration) for most cases, though for at least
two operating conditions predicted ozone residual was significantly different from
measured residual. The authors suggested poor agreement in those cases might have
225
been the result of variation in water quality during experiments or might have been
related to their model’s simplifying assumptions. They also suggested that backmixing
strongly influences bromate formation, which suggests the ADR model, which does not
formally incorporate backmixing, may not be the optimal model for use in predicting
bromate formation in full scale reactors.
A schematic diagram showing the full-scale contactor is provided in Figure 74.
Reactor dimensions and other design data were taken from a published study of the
hydrodynamics and disinfection efficiency of the full scale reactor (Mariñas et al., 1999).
The two, two-phase chambers are operated in countercurrent mode. Based on data
presented in one study of the full scale reactor (Tang et al., 2005), the ozone generator
feed gas is dried air and gas to liquid flow ratio in the reactor varied between 0.083 and
1.4. Gas was injected through fine pore diffusers. The shape and spacing of the diffusers
were not reported.
In the rough (two dimensional) CFD model developed for the reactor shown in
Figure 74, several simplifications of reactor geometry were made. The simplifications
were made because detailed design data were not available. Had these data been
available, developing a more accurate model geometry and improved mesh would have
been straightforward and would not have resulted in significant increases in the CPU time
required to generate solutions.
226
6.77 m
2.36m
0.92m
2.44m
0.92m
0.92m
0.92m
1.98m
1.98m
1.98m
0.84m
Waterintake
Diffusers
Discharge
Figure 74: ACWD Full Scale Reactor Schematic Diagram
VII.2 Full Scale Reactor CFD Model
VII.2.1CFD Model General Features
The major features of the full scale reactor CFD model were largely the same as
those of the laboratory reactor CFD model:
Two phase flow was modeled using an Eulerian-Eulerian treatment.
Bubbles were assumed monodisperse with a bubble diameter of 2.5 mm.
Bubble drag was calculated using the Grace drag model and ozone mass transfer was
calculated using the Higbie mass transfer model.
Dirichlet (specified normal velocity) boundary conditions were used for the water and
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gas intakes; a pressure boundary condition was applied at the water discharge. The
water free surface was specified as a “degassing” boundary (free-slip boundary for
the liquid flow, zero gradient boundary for the gas phase).
A schematic diagram showing the CFD model is presented in Figure 75.
Symmetry planeWater inlet(specified normalvelocity andCryptosporidiumparvum numberdensity)
Gas inlet (specifiednormal velocity andO3 concentration)
Degassing boundary at water surface
Water discharge(specifiedpressure)
Figure 75: Full Scale Reactor CFD Model Schematic Diagram
To reduce computation time, only half the reactor was modelled and a symmetry
boundary condition was imposed at the reactor midplane, as shown in Figure 75. A
relatively coarse unstructured mesh with a total of 704,200 elements was employed.
Elements were clustered near the inlet, the spargers and the underflows/overflows of the
baffles.
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VII.2.2Cryptosporidium Inactivation and Bromate Formation Submodels
In the CFD model, scalar transport and reaction rate expressions were included
for ozone decay, ozone demand (by natural organic matter [NOM]), bromate formation
and Cryptosporidium parvum inactivation. Reaction rate expressions for all of these
constituents were those reported by Tang (2005) and presented below.
Ozone demand was modeled with first-order kinetics and, based on batch ozone
decay studies, the decay constant was -1s001.0011.03
Ok . The authors modeled
bromate formation as first order with respect to ozone concentration. Based on semi-
batch ozonation studies, the rate constant for bromate formation was estimated to be 9.4
10-5 s-1. Though the bromate formation model and rate constant are consistent with data
collected in batch experiments, their utility for waters other than those tested seems
unlikely, since the bromate formation rate is not dependent on raw water bromide or
ammonia concentrations.
C parvum inactivation was assumed to follow Chick kinetics (overall second
order, first order in both ozone concentration and C parvum oocyst density). Based on Ct
values in the LT2ESWTR (Table 1), the rate constant was TNk 097.10917.0 , where T
is temperature in °C.
Rate expressions for ozone decay, ozone demand, bromate formation and C.
parvum inactivation are summarized in Table 23.
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Table 23: Rate Expressions and Constants, Full Scale CFD Model
Reaction Rate expression Rate constant Notes
Ozonedecay 33
3
OO
OCk
dt
dC
-1s001.0011.03
Ok Batchexperimentsperformed at20°C
Ozonedemand NOMNOM 3
3 CCkdt
dCO
O
s-mg/L16.020.3NOM k Approximationdeveloped toensure demandoccurs muchfaster thandecay andinactivation
Bromateformation 33
3
BrO
BrO
OCkdt
dC
-15BrO s109.4
3
k Developedbased on batchexperiments.Initial bromideconcentrationnot reported
C. parvuminactivation NCk
dt
NdON 3
min-mg/L097.10917.0
3O
TNk Based on Ct
tables ratherthan batchexperiments
VII.3 Phase Distribution and Flow Field
Gas volume fraction contours predicted by the CFD model for the reactor
operating at a gas flow rate of 404 standard cubic meters per hour and a liquid flow rate
of 15.5 MGD (2.01 m3/s) are presented in Figure 76 -Figure 78. Gas volume fraction is
the volume occupied by gas within a given reactor volume. Figure 76 shows gas volume
fraction on a vertical plane at the midsection of the computational domain. The bubble
plumes from the individual diffusers do not rise straight upward. Rather, they are drawn
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toward the reactor headwall and coalesce as they rise. The tendency of bubble plumes to
be drawn toward walls and coalesce is consistent with the experimental observations of
Freire et al. (2002). Another factor in the deflection of the bubble plume toward the
headwall is the large clockwise circulation generated in the dissolution chamber by the
horizontal introduction of water to the chamber. This phenomenon is illustrated below.
Figure 76: Gas Volume Fraction Contours, Full Scale Reactor, Vertical Plane
The distribution of gas on a horizontal plane near the sparger and on a horizontal
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plane at the midheight of the reactor are shown in Figure 77 and Figure 78, respectively.
These figures show the migration of the bubble plume toward the center of the reactor
(due to coalescence of bubble plumes) and the presence of large vortices (diameter on the
order of the chamber length) in the dissolution chamber. The gas volume fraction
contours show a non-uniform and three dimensional distribution of gas in the reactor.
Figure 77: Gas Volume Fraction Contours, Full Scale Reactor, Horizontal Planenear the Spargers
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Figure 78: Gas Volume Fraction Contours, Full Scale Reactor, Horizontal Plane atthe Reactor Mid-height
Superficial velocity vectors on a vertical plane in the first 6 and last 6 chambers of
the reactors are shown in Figure 79 and Figure 80, respectively. In the vector plots, the
magnitude of the vector is indicated by its color and vectors were not projected onto the
plane.
In the ozone dissolution chamber (with the diffusers on the bottom, the
momentum of the influent water stream creates several large recirculations whose length
scales are on the order of the chamber width, as seen in Figure 79. There is a strong
upward flow along the reactor headwall and a strong downward flow of liquid at the
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upstream face of the first baffle. In the second large chamber, circulation is also
pronounced and water follows a serpentine path as it traverses the reactor. In subsequent
chambers (shown in Figure 80) the water flow path becomes better defined, tending to
flow preferentially at the upstream face of each baffle. The hydrodynamics illustrated in
Figure 80 deviate significantly from plug flow. In the final 5 chambers the main water
flow path occupies less than half the available cross sectional area and there are large
recirculating regions present in each chamber. As shown below, the presence of the
preferential flow path results in short circuiting of pathogens past treatment and the
presence of recirculating regions results in prolonged contact between bromide and ozone
and contributes to bromate formation.
Tracer studies performed by Tang et al. indicate that in the AWCD ozone bubble
contactor, the ozone dissolution chambers behave as CSTRs. This result supports the
approach proposed by Lev and Regli (1992b) of treating bubbled chambers as CSTRs in
assigning Ct credit. This result also indicates that conditions conducive to higher than
expected bromate formation exist (Tang et al., 2005), though in the prior study no
rigorous modeling or experimental work provided conclusive evidence that these
recirculating regions are indeed bromate formation “hot spots.”. The fluid recirculating
in the center of the dissolution chambers has a high residence time and potentially a high
ozone concentration.
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Figure 79: Water Superficial Velocity Vectors, Chambers 1 - 5, Full Scale Reactor
Like serpentine horizontal reactors, the 180 turns employed in the full scale
reactor design produce dead zones and large recirculations that reduce the effective
chamber cross sectional area and cause flow to deviate from plug flow, even in the
narrow chambers in which net water flow is upward. To improve non-ideal
hydrodynamics such as those seen in Figure 79 and Figure 80, engineers usually modify
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under-over baffle reactors by modifying baffle spacing (Cockx et al., 1999; Do-Quang et
al., 1999), modifying baffle gap distance (between the baffle and reactor floor) (Henry
and Freeman 1995), or by adding partial baffles that may be solid or perforated
(Heathcote and Drage 1995).
Figure 80: Water Superficial Velocity Vectors, Chambers 6 - 10, Full Scale Reactor
236
Figure 81: Water Superficial Velocity Vectors, Full Scale Reactor, HorizontalPlane, Chambers 1 – 4, Projection Tangential to Plane
237
Figure 82: Water Superficial Velocity Vectors, Full Scale Reactor, HorizontalPlane, Chambers 5 – 10, Projection Tangential to Plane
VII.4 Inactivation and Comparison to Log Credits from Ct Models
CFD predictions for ozone residual, bromate concentration and Cryptosporidium
oocyst number are presented in Figure 83, Figure 84 and Figure 85, respectively.
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Figure 83: Dissolved Ozone Concentration Contours, Full Scale Reactor
As measured in the full scale contactor (Tang et al., 2005), ozone residual at the
reactor discharge is less then 0.05 mg/L. The predicted ozone residual profile seen in
Figure 83 indicates that full advantage is not being used of the reactor volume. Because
no Ct credit is awarded for the first chamber (the only chamber with a high discharge
ozone residual), the only chamber contributing significantly to Ct is the second chamber
in which ozonated air is bubbled. From a Ct credit standpoint, a better operating
condition would be application of only enough ozone to overcome fast demand in the
first chamber and increasing ozone application in the second bubbled chamber. This
approach would result in higher ozone residual in the last 6 chambers of the reactor. For
239
the first ozone dissolution chamber, the regulatory approach of not allowing any
disinfection credit presents a disincentive to good design (i.e., ozone application in the
two chambers that maximizes transferred dose and mixing) and is inconsistent with the
observation that significant disinfection can take place in a chamber that has low or no
measurable ozone residual in its effluent (Xu et al., 2002). Regardless of the point of
application of ozone, ozone decay is a serious problem in this reactor.
Because bromate formation rate was modeled as first order with respect to ozone
residual, bromate contours, shown in Figure 84, are similar to ozone contours. The small
region of low bromate concentration water in the discharge pipe is a result of the choice
of an entrainment boundary condition. For an entrainment boundary, pressure gradient is
set equal to zero and concentration of scalar species for fluid flowing into the boundary is
specified (in this case, influent bromate concentration was set equal to zero). Because the
low bromate concentration is confined to the discharge pipe, the boundary condition does
not influence conditions within the reactor and is considered adequate.
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Figure 84: Bromate Concentration Contours, Full Scale Reactor
Recirculating regions are bromate-formation hot spots. This is evident in the
bubbled chambers, both of which have large high bromate concentration regions in their
centers. Bromate formation in the last 5 chambers of the reactor is minimal, because
ozone residual is low. Predicted bromate formation does not exceed the MCL of 10
g/L, though if higher ozone residual were realized in the reactor, the production of
bromate would be higher.
Cryptosporidium parvum density contours, seen in Figure 85, indicate that
log removal of microorganisms is high for water detained in recirculations in the two
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bubbled chambers and
significant short circuiting exists non-bubbled chambers.
The first observation is consistent with the assumptions used in development of
methodology for determining reactor Ct. The second observation indicates that, despite
their common use, under-over baffled reactors employing 180 turns are prone to dead
zones in the corners of the turns and large recirculations in all chambers. These dead
zones and recirculations reduce the volume of reactor available for the main liquid flow
and promote short circuiting. Short-circuiting, in turn, reduces contact time between
microorganisms and disinfectant.
Suboptimal hydrodynamics related to flow through 180 turns occurs in single-
phase serpentine chlorine contactors and other chemical disinfection processes as well as
in ozone bubble contactors. Systematic study of design modifications that improve
hydraulics in such arrangements would be a general benefit to the water treatment
industry.
242
Figure 85: Cryptosporidium parvum Density Contours, Full Scale Reactor
243
VIII CONCLUSIONS AND DISCUSSIONS
VIII.1 Summary of Major Findings
Three gas flow rate ranges within the ideal bubbly flow regime were identified in
which the variation in Peclet number with gas flow rate differed. At low gas flow
rates, Peclet number falls sharply with gas flow rate. At intermediate gas flow rates
Peclet number does not vary with gas flow rate. At high gas flow rate Peclet number
falls with increasing gas flow rate.
CFD “virtual tracer” studies agreed very well with measured tracer concentrations.
CFD analyses predict large vortices are present at the column walls in the vicinity of
the sparger. These vortices cause back-mixing of the liquid stream and elongate as
gas-to-liquid flow ratio is increased.
CFD and mass transfer visualization experiments demonstrated that mixing is non-
uniform in the column. High-intensity mixing occurs at the bottom of the reactor,
which may be regarded as a completely mixed reactor. The length of this well-mixed
region increases with increasing gas-to-liquid flow ratio.
Outside the well-mixed zone, Stanton number increases with increasing gas-to-liquid
flow ratio.
VIII.2 Details of Major Findings
Two series of experiments were conducted to quantify mixing in countercurrent
bubbly flow, investigate spatial variations in mixing and mass transfer and explore the
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advantages of CFD over lower fidelity models such as the ADR and CSTR reactor
models for adequately reproducing phenomena observed in experiments. The anticipated
benefits associated with these goals were improved bubble contactor designs more
consistent with countercurrent hydrodynamics and better modeling leading to informed
management of acute and chronic health risks associated with drinking water
contaminants.
Tracer studies performed over a range of gas flow rates identified three gas flow
rate ranges in which mixing (Peclet number) variation with gas flow rate differed. For
gas flow rate below 1.0 slpm, Peclet number fell sharply with increasing gas flow rate. In
the gas flow range 1.0 to 2.25 slpm, Peclet number remained constant at 3.0. This
finding was consistent with that of one prior study of mixing in countercurrent flow
bubbly flow. Above gas flows of 2.25 slpm, Peclet number fell with increasing gas flow
rate, following trends predicted by two other prior researchers.
CFD “virtual tracer studies” agreed well with experimental tracer studies and
mixing intensity predicted in CFD analyses of countercurrent flow also matched
dispersion estimates made in residence time distribution analyses. Peclet number
predicted in CFD analyses for the same range of gas flow rates as tracer studies agreed
very well with experimental data, especially for gas flow rates at and above 0.5 slpm.
CFD analyses also provided insights into the flow field and variation of mixing intensity
with height. In the vicinity of the sparger, large vortices are produced by the shear of the
down-flowing liquid by the up-flowing bubble plume. As gas flow rate is increased,
245
these vortices elongate and the bubble plume changes from relatively straight and wide to
wavy and narrow as it rises in the column. The large vortices near the sparger back-mix
the liquid phase, making the region near the sparger well-mixed, despite poor distribution
of phases.
CFD showed the variation in mixing in the reactor to be non-uniform, with much
more intense mixing in the bottom of the reactor (near the sparger) than in the top of the
reactor. This distribution of mixing intensity would be changed significantly if inlet and
discharge configuration were different than those of the laboratory reactor. There are two
implications related to the importance of inlet and discharge configurations. First, in
addition to other scale-up laws, the influence of inlet and discharge configuration on pilot
column hydrodynamics must be considered when scaling to full scale. Second, if poor
hydraulic performance is realized in an ozone bubble contactor (e.g., T10 / is very low
or large fluctuations in ozone residuals occur at the reactor discharge), modifications to
inlets and discharges for chambers within the reactor offer relatively low-cost means of
improvement. Assessment of alternative modifications with a validated CFD model prior
to implementation could provide quantitative data on the effect of the alternatives faster,
cheaper and with more detail than experiments such as tracer studies or flow visualization
experiments.
A technique employing a reactive dye (indigo dye) and digital photography was
devised for allowing visualization of mass transfer and investigation of spatial variations
in mixing and mass transfer in the reactor. Inspection of images produced using this
246
technique produced the following observations:
Indigo dye concentration and ozone dose can be selected to yield wide variation in
indigo dye concentration in the reactor.
In images of indigo dye flowing in the reactor, digital image pixel color varies
linearly with indigo dye concentration for indigo dye in the concentration range 0.5 to
6.5 mg/L.
Indigo dye decolors steadily and uniformly as water flows downward in the top of the
reactor.
Lower in the reactor, there are significant variations in indigo dye concentration at a
given reactor axial location.
Throughout the reactor, liquid flow occurs in two zones – upward flow in the bubble
plume and downward flow near the cylinder walls. Flow in the reactor is three
dimensional and unsteady, swirling and exhibiting chaotic motions. In the bottom of
the reactor, decoloration of indigo dye occurs as eddies of dye-rich water from the
downward flow are entrained into the bubble plume and decolored. Had aqueous
ozone not been immediately consumed by indigo dye, ozone concentration in the
bubble plume (and driving force for ozone mass transfer) would have been higher and
mass transfer in the vicinity of the bubbles would have been retarded.
Near the bottom of the reactor (near the sparger), there is a zone in which indigo dye
color is more or less uniform, indicating the liquid contents of that zone are well
247
mixed. This zone is referred to as the entrance zone and its length increases with gas
to liquid flow ratio. As seen in CFD studies, this entrance zone is comprised of a
central upward flowing region (the bubble plume) driving large vortices between the
bubble plume and reactor walls.
To allow estimation of Peclet number, Stanton number and entrance zone length,
indigo concentration data from digital images were radially-averaged and the results were
fit using two models: a one-zone model in which the entire reactor was modeled using the
ADR model and a two-zone model in which the zone near the sparger was modeled as a
CSTR and in the upper zone the ADR model was used. Because data dependence could
not be disproved when the radially-averaged data were fit with the single zone model, it
was demonstrated that there are two distinct zones of different dispersion and perhaps
different mass transfer coefficient in the reactor. This finding is significant given the use
of single zone ADR or CSTR models for bubble column flows in pilot studies, full scale
reactor analyses and regulatory compliance.
Entrance region length increases with gas to liquid flow ratio. This finding is
consistent with CFD predictions that increasing gas flow rate stretches the large vortices
present in the vicinity of the sparger. At a gas to liquid flow ratio of 0.1, the entrance
region occupies nearly 40% of the reactor height. Future experiments should be directed
at determining the dependence of entrance length on water depth in the reactor. It is
hypothesized that entrance region length should be independent of water depth; since
momentum exchange between the bubble plume and downward flowing liquid
248
establishes the vortices that define the entrance region, the entrance length should be
dependent on gas and liquid flow rates (momentum) and independent of water depth in
the reactor.
Stanton number increases with increasing gas to liquid flow ratio. Two
phenomena likely play roles in this trend. Higher gas flow rates result in both higher
specific surface area and increased turbulence and dispersion generated in bubbles’
wakes. In order to determine the roles these phenomena play in dependence of mass
transfer on gas to liquid flow ratio, the gas phase holdup must be measured. For the
reactor used in the current study, gas phase holdup at 5 points in the reactor could be
made using a differential pressure sensor. For a two dimensional reactor, gas phase
holdup could be estimated through analysis of digital photographs. Such an analysis
would involve bubble identification using particle identification techniques and summing
of bubble volumes within regions of the reactor.
Trends of Peclet number with gas to liquid flow ratio could not be determined
conclusively. All Peclet number estimates from indigo dye experiments followed trends
observed in RTD analyses except a single, low gas to liquid ratio datum at which Peclet
number was significantly less than expected. Indigo dye may have been completely
depleted in portions of the reactor in the experiment from which the anomalous Peclet
number was estimated.
As with mixing investigations, CFD analyses yielded details and insights into
countercurrent flow mass transfer. Most important, using an uncalibrated mass transfer
249
model, the CFD model was able to accurately predict the variation in indigo dye
concentration in the reactor over the entire range of liquid and gas flow rates studied.
This agreement indicates that despite use of a two-equation turbulence model prone to
numerical dispersion, the CFD model predicted mixing of the main liquid flow with the
bubble plume sufficiently. Improvement in mass transfer and mixing predictions can be
expected if a higher-resolution turbulence model such as LES (large eddy simulation)
were used.
CFD simulations predicted and explained an increase in indigo concentration in
the vicinity of the sparger observed in numerous mass transfer visualization images.
Near the sparger, indigo dye rich water from the reactor walls is back-mixed into the
middle of the reactor, resulted in an apparent increase in indigo dye concentration.
VIII.3 Using CFD in Design and Scale-up of Ozone Bubble Contactors
Common use of the advection-dispersion-reaction (ADR) model (LeSauze et al.,
1993; Zhou and Smith 1994; El-Din and Smith 2001(a); Kim et al., 2002b; Kim et al.,
2005) and the CSTR model (US EPA Office of Drinking Water 1991; LeSauze et al.,
1993; Roustan et al., 1996; US EPA Office of Water 2003) for pilot and full scale ozone
bubble contactors implies that in countercurrent flow, phases are uniformly distributed
and contact between phases is uniform. The current study has shown that this is not the
case, even in the relatively simple tall cylindrical bubble column in which experiments
were performed. This discrepancy between models and hydrodynamics is significant –
modeling reactors as CSTRs provides a conservative estimate of inactivation in full scale
250
ozone bubble contactors (Lev and Regli 1992a; Lev and Regli 1992b) but leads to
designs prone to unnecessary bromate production (Tang et al., 2005).
As an alternative to the ADR and CSTR models, CFD can deliver realistic
estimates for microbial inactivation and for chemical species whose rate of production
can be dependably represented by a set of elementary reactions or a global reaction
expression. These CFD models can be developed using mass transfer and bubble
transport submodels drawn from empirical and semi-empirical studies and using batch
kinetic data for chemical species and microorganisms. Unlike models such as the ADR
which are calibrated using data from pilot studies, CFD models are based on first-
principles submodels and have validity for reactors of virtually any geometry.
Application of CFD should no longer be limited to modeling and design of unit
process operations in very high production plants, as has been the tendency in the past.
The resources for producing the CFD models for this thesis (one student under the
direction of knowledgeable managers, a desktop computer and a software license) are
modest, making CFD accessible, either in-house or through subcontracts, to small utilities
in need of improved hydrodynamics, bromate production or design of new disinfection
unit operations.
Incorporation of CFD into pilot studies will allow improved scale-up to full scale.
As demonstrated in this study, RTD analyses, the most common technique used in pilot
reactor hydrodynamics characterization, is not suited to identifying important flowfield
features such as the well mixed zone in the reactor bottom, the large recirculating flows
251
in the vicinity of the sparger, or the flow structures associated with inlets and outlets.
The inlet and outlet configuration may dominate pilot reactor hydrodynamics, as seen in
the Philadelphia Water Department pilot reactor. Given the importance of inlet and
discharge configuration, it would be advisable to perform CFD analysis as a part of the
pilot reactor design process.
Accurate depiction of hydrodynamics is important for accurate prediction of the
progress of chemical reactions in continuous flow reactors (Hermanowicz et al., 1999;
Tang et al., 2005). When chemical reactions are modeled as a sequence of elementary
reactions and the fate and transport of intermediate species is included in a CFD model,
CFD more accurately predicts the production/consumption of chemical species than
lower-fidelity models because chemical reactions occur based on the local concentration
of all species. There is a limit to the ability of CFD to incorporate species into a chemical
reaction model – each species adds to CPU time requirements of a solution and very
short-lived species or species whose reaction rate is very fast require very small time
steps to avoid numerical instability or overflows.
Finally, it is noted that most ozone bubble column reactors are similar in design.
Nearly all ozone contactors have over-under baffle arrangements and similar density of
spargers on the reactor floors. CFD could be used in a general exploration of the
influence of reactor geometry and operating conditions on hydraulic and disinfection
performance of reactors with different chamber aspect ratios, sparger spacings, baffle
configurations, gap widths, etc. A systematic study of these design parameters might
252
yield guidelines for preliminary reactor designs and information helpful in scale-up from
cylindrical pilot reactors to full scale.
A specific design modification that should be investigated is exploration of the
impact of minor tilts in reactor walls on mixing in ozone contact chambers. As seen in
the current work and a prior study (Rice and Littlefield 1987), minor misalignment of a
tall cylindrical bubble column away from vertical can increase mixing by an order of
magnitude. A reactor designed to take advantage of this phenomenon would be a
significant improvement of existing reactors because vigorous mixing would promote
more even distribution of phases which, in turn, would result in greater mass transfer
rates and less propensity for the liquid phase to short circuit in ozone dissolution
chambers.
VIII.4 Critical Review of Ozone Mass Transfer Visualization Technique
The mass transfer visualization technique demonstrated in this study allowed
observation of spatial variation in mass transfer rate at a resolution heretofore unreported
in the literature and permitted estimation of a gas entrance length region.
Subsequent studies employing the mass transfer visualization technique can
benefit from several modifications.
Use of a two-dimensional reactor. The reactor used in this study was designed to be
comparable to pilot ozone bubble contactors used in prior studies and to promote, as
nearly as possible, axisymmetric flow. Though these goals were met in the reactor
253
design, the curvature of the reactor distorted color near the reactor walls. Subsequent
studies might employ a tall, thin right rectangular cylindrical reactor. In such a
reactor, a rod sparger or different numbers and spacings of spherical spargers could
be employed. In addition to yielding better digital images, this design could be
modeled with a simpler CFD mesh (multi-block structured grid) and would allow
easier comparison of CFD results with images from mass transfer visualization
experiments.
Improved background lighting. An alternative lighting scheme that might provide
more intense, uniform lighting is shown in Figure 86. Optimization of this scheme
will require experimentation with the number and spacing of fluorescent tubes and the
thickness and material of the translucent plastic sheet.
254
Translucent plastic sheet
High temperature fluorescent lamps
Reactor
Light baffles
Figure 86: Alternate Lighting Scheme
Performing all experiments at a single ozone generator voltage and indigo dye
concentration. The rationale for choosing the ozone voltage used in the experiments
in this study were achieving the greatest change in indigo dye color without
completely decoloring the dye within the reactor. Since the optimal voltage was not
known precisely for each experiment, multiple cases were run at different voltages for
some operating conditions. Influent indigo dye concentration also varied between
experiments. These variations in ozone dose and intake indigo dye concentration
made direct comparison of mass transfer (indigo consumption) from case to case
difficult. Based on the results of the indigo dye mass transfer visualization method
reported in this dissertation, future researchers should be able to select an adequate
255
ozone generator voltage and indigo dye concentration for all experiments.
VIII.5 Balancing Acute and Chronic Risks
As outlined in section Chapter I, it is difficult to design reactors that afford a high
level of disinfection while not producing a harmful concentration of disinfection by-
products. Relatively long detention times provide a factor of safety and ensure
disinfection occurs to a desired level; relatively short residence times diminish
disinfection by-product formation. Balancing the acute microbial risks with chronic risks
from by-products may require more detailed understanding of the interaction of
hydrodynamics, chemistry and microbiology than has traditionally been established prior
to design of ozone bubble columns. Here, balancing means designing reactors with a
distribution of residence times that are long enough to ensure sufficient disinfection, but
not so long that excessive disinfection by-product formation occurs.
Hydrodynamics in bubble column reactors are complex and have a strong
influence on both microbial inactivation and disinfection byproduct formation. The
preceding work demonstrated that, because bubbled chambers tend to behave as CSTRs,
the US EPA’s approach of assigning Ct credit assuming CSTR behavior is justified and
does provide a conservative estimate of microbial inactivation. It also demonstrated that
in regard to bromate formation, producing reactors whose chambers behave as CSTRs is
not a conservative approach and is not protective of chronic risks from chemical
contaminants.
256
The first step in balancing acute (microbial) and chronic (DBP) risks in fine
bubble ozone contactors is improved modeling and identification of hydrodynamics and
reactor designs that promote DBP formation. CFD is the only analysis available today
that incorporates all necessary processes with the level of detail needed to accurately
predict microbial inactivation and disinfection byproduct formation.
The second step is to design reactors with hydraulics in contact chambers closer
to plug flow. Developing such reactors will require experimentation. Tracer studies
have been used effectively in analysis of reactor hydraulics, but do not provide definitive
or specific information about the direction fluids flow in a given region in a reactor, so it
is recommended that experimentation be accompanied by CFD analyses. CFD modeling
can be less expensive than experimentation and could enable a wider range of design
alternatives.
Finally, current regulations and guidelines favor design of reactors that behave as
CSTRs. This approach is protective of acute risk but not chronic risk. Allowing use of
alternative models (beyond those permitted in the LT2ESWTR) for assessing disinfection
efficiency could encourage development of reactors designed to promote disinfection and
minimize DBP formation.
257
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271
APPENDIX A: LIST OF SYMBOLS
Variable Description
a Specific interfacial area
A Area
Bo Bond number
CD Drag coefficient
CI Indigo dye mass concentration
3OC Dissolved ozone mass concentration
dB Bubble diameter
Di Binary diffusion coefficient of species i
E Axial dispersion (L2/T)
E(t) Expectation
Eo Eotvos number
F Normalized tracer concentration
g Gravitational acceleration
Ga Galileo number
H Reactor height
IT Turbulent kinetic energy intensity
3BrOk Bromate reaction rate coefficient
kL Liquid side mass transfer coefficient
kN Microbial inactivation rate coefficient
3Ok Ozone autodecomposition reaction rate coefficient
m Henry’s law constant (dimensionless)
Mo Morton number
N Microorganism number density
NS Stanton number
P Pressure
Pe Peclet number
272
Variable Description
TP Turbulent kinetic energy dissipation rate
Q Volumetric flow rate
Re Reynolds number
S Stripping factor
Sc Schmidt number
Sh Sherwood number
t Time
T10 Time for passage of 10% of pulse of conservative tracer
UG Gas superficial velocity
UL Liquid superficial velocity
U
Velocity
V Volume
vB Bubble terminal rise velocity
We Weber number
z Depth
z* Normalized depth
G Gas hold-up
Surface tension
Density
Kinematic viscosity
Dynamic viscosity
T Turbulent viscosity
G Gas volume fraction
273
APPENDIX B: LIST OF ABBREVIATIONS AND ACRONYMS
Variable Description
ADR Advection-Dispersion-Reaction
CFD Computational Fluid Dynamics
CSTR Completely Stirred Tank Reactor
Ct Product of ozone residual concentration and time
DBP Disinfection Byproduct
HAA Haloacetic Acid
HDT Hydraulic Detention Time
LT2ESWTR` Long Term 2 Enhanced Surface Water Treatment Rule
NOM Natural Organic Matter
SWTR Surface Water Treatment Rule
TA Total Alkalinity
TOC Total Organic Carbon
USEPA United States Environmental ProtectionAgency
274
APPENDIX C: ANALYSIS OF RADIALLY-AVERAGED IMAGE DATA
Radially-averaged indigo dye image data were used to estimate dispersion and
mass transfer rate in the column. The presence or absence of multiple zones was
determined via comparison of fit of single- and multiple-zone models to data.
Several models were formulated based on observed trends in indigo dye
consumption. At relatively high gas to liquid flow ratios, indigo dye concentration
reduced monotonically in the top of the reactor and was constant in the bottom of the
reactor. This observation prompted the formulation of the one-zone and two-zone
models described below. In the one-zone models, the mass transfer rate and dispersion
are assumed uniform in the reactor. In two-zone models, the bottom of the reactor is
assumed to behave as a continuously stirred tank reactor (CSTR) and it is assumed the
top of the reactor can be modeled as a 1-dimensional axial flow with dispersion and
reaction (1-D ADR) reactor. In one formulation of the two-zone model, the mass transfer
rate in the CSTR portion of the reactor is assumed to be different from that in the top half
of the reactor. In a second formulation, the mass transfer rate is assumed the same in the
top and bottom of the reactor and the difference in observed mass transfer in the two
regions is attributed wholly to difference in mixing.
Derivation of the single-zone and two-zone models follows.
Single-zone model
Conservation of gas phase ozone and aqueous indigo dye are depicted in Figure
275
87. Gas phase dispersion (back-mixing of bubbles) is assumed to be negligible and
dissolved ozone is assumed to react very quickly with indigo dye.
dzACCak OOL aq*
g 33
zgOg CU *
3
dzzgOg CU
*
3
dz
z
dzACCak OOL aq*
g 33
zgOg CU *
3
dzzgOg CU
*
3
dz
zz
(a) Conservation of gas phase ozone (b) Conservation of aqueous indigo dye
dzA
dt
Cd
M
MR
gO
O
II
*
3
3
z
II
zIL
dz
dCD
CU
dz
dzz
II
dzzIL
dz
dCD
CU
z
dzA
dt
Cd
M
MR
gO
O
II
*
3
3
z
II
zIL
dz
dCD
CU
dz
dzz
II
dzzIL
dz
dCD
CU
zz
Figure 87: Conservation of Gas Phase Ozone and Aqueous Indigo Dye
Conservation of gas phase ozone
Conservation of mass about the control volume depicted in Figure 87(a) can be
written
dzCmCakCQCQ OGOLdzzGOGzGOG aq3333
where A is the column cross sectional area, QG is gas volumetric flow rate
(positive upward), kL is mass transfer coefficient (dimensions L/T), a is specific surface
276
area (surface area per unit volume of reactor; dimensions L-1), GOC3
is gas phase ozone
mass concentration, aqOC3
is aqueous phase ozone mass concentration and m is the
Henry’s law constant (equilibrium gaseous ozone concentration equilibrium aqueous
ozone concentration). Henry’s law constant is calculated via the relation (Perry and
Chilton 1973) in equation 70 (repeated below)
C5C51687
2.6
C5C5840
25.3log
TT
TTm (70)
where T is temperature in degrees Kelvin and m is dimensionless.
Since the ozone-indigo dye reaction is very fast, aqueous ozone does not
accumulate and the conservation equation becomes
GO
G
LzGOdzzGOC
Um
ak
dz
CC
3
33
)(
)(
3
3
GO
G
LGO CUm
ak
dz
Cd (A-1)
Define Stanton number, stripping factor and dimensionless height as
;L
LS
U
HakN (A-2)
;L
G
U
UmS and (A-3)
277
H
zz * . (A-4)
Equation A-1 becomes
*
)(
)(
3
3 dzS
N
C
CdS
GO
GO (A-5)
Equation A-5 is integrated from z* to the reactor bottom (z* = 1; gas injection
point). Denoting the gas injection ozone concentration as 03 GOC , the integration of
equation A-3 proceeds as follows:
*0
1
*
1ln
ln
3
3
*
03
33
zS
N
C
C
zS
NC
S
GO
GO
z
SC
CGO
GO
GO
*
33
1
0
zS
N
GOGO
S
eCC
and
*
33
1*
0*
zS
N
GOGO
S
eCC
(A-6)
where
m
CC
GO
GO3
3
* (A-7)
278
Conservation of aqueous indigo dye
Conservation of indigo dye, depicted in Figure 87(b), can be written
dzARCQz
CDACQ
z
CDAdzA
t
CIdzzIL
dzz
I
zIL
z
II
where QL is liquid volumetric flow rate, CI is indigo trisulfonate concentration, D is
dispersion and RI is rate of indigo consumption. Assuming steady state conditions in the
column and that the ozone-indigo reaction is fast enough that rate of consumption of
indigo dye is equal to the mass transfer rate of ozone and noting that liquid superficial
velocity, UL, is equal to QL/A, the conservation of indigo dye can be written
dzCakM
M
dz
CCU
dz
dz
Cd
dz
Cd
D GOL
O
IzIdzzI
Lz
I
dzz
I
*
3
3
Substitute the expression from equation A-6 for *
3 GOC and, as dz 0, the
conservation of indigo dye becomes
*
3
3
1*
02
2 zS
N
GOL
O
IIL
I
S
eCakM
M
zd
CdU
zd
CdD
Introduce the dimensionless parameters z* = z / H and *IC =CI / CI 0, where CI 0 is indigo
dye concentration in the reactor feed. The nondimensionalized conservation of aqueous
indigo dye becomes
279
*
3
3
1
0
*0
*
*
2*
*2z
S
N
LS
I
GO
O
IILIS
eD
HUS
S
N
C
C
M
M
zd
Cd
D
HU
zd
Cd
Define Peclet number and the parameter as
D
HUP L
e (A-8)
0,
0
0,
0 3
3
3
3 I
gO
L
G
O
I
I
gO
O
I
C
C
Q
Qm
M
MS
C
C
M
M (A-9)
Conservation of aqueous indigo dye becomes
*1
*
*
2*
*2 zS
N
eSI
eI
S
ePS
N
zd
CdP
zd
Cd
(A-10)
Equation A-10 is integrated as follows.
*1*
*
*
*
zS
N
eS
IeI
S
ePS
NCP
zd
Cd
zd
d
*1*
*
* zS
N
eIeI
S
ePCPzd
Cd(A-11)
where is an integration constant. Equation A-11 is solved using an integrating
factor:
280
***
*
***
*
**
1*
1*
*
1*
*
zP
e
zS
NzP
eS
eI
zP
zS
N
ezP
IzP
zS
N
ei
zPdzP
e
Se
e
S
ee
S
ee
eP
ePSN
PCe
ePeCedz
d
ePpCpdz
d
eep
**1* zP
e
zSN
eS
eI
eS eP
ePSN
PC
(A-12)
and the rate of change of indigo dye concentration with respect to axial location is:
dCI*
dz*
NS S Pe
NS S Pe
e
NS S 1 z* Pe ePe z*
(A-13)
Determining integration constants for single zone model
Equation 11 is solved subject to a Dirichlet inlet boundary condition (CI = CI,0 at
z* = 0) and Danckwerts boundary condition at the outlet (dCI / dz*|z=1=0) (Nauman and
Buffham 1983; Teefy and Singer 1990; Haas et al., 1998). At the reactor discharge,
01
*
*
*
z
I
zd
Cd
ePe
eS
eS ePPSN
PSN
0
eP
eS
S ePSN
SN
281
Substitute β into the expression for indigo dye concentration (equation A-11) and
simplify.
**1* zPP
eS
S
e
zSN
eS
eI
eeS eePSN
SN
Pe
PSN
PC
e
zPS
zSNe
eS
IP
eSNePPSN
C eS
** 11* (A-14)
A Dirichlet boundary condition is applied at the top of the reactor (z* = 0):
10
**
zIC (A-15)
e
PS
SNe
eS PeSNeP
PSNeS
1
eS P
SSN
e
eSe
eSNePPSNP
1
Substitute the expression for into equation 15 for the final expression for
aqueous indigo dye concentration.
eSe P
SSN
ezP
SzS
e
eS
I eSNePeSNePPSN
C
** 11* 1
**
111* zPPS
zSNSNe
eS
IeeSS eeSNeeP
PSNC
(A-16)
In the limit eS PSN , equation A-16 becomes indeterminate and an expression for
282
dimensionless indigo dye concentration is determined using L’Hopital’s rule.
1
11lim
11lim
**
**
1* zPPzSNe
SNe
eS
eS
zPPS
zSNSNe
eS
eeSS
eeSS
eeePzeP
PSN
PSN
eeSNeeP
PSN
Substituting this result into equation A-16 yields the final expression for dimensionless
indigo dye concentration in the limit eS PSN :
e
PzPee
I PeezPPC
ee
ePS
SN
111*
lim
1*
*
(A-17)
Derivation of Governing Equations, Two Zone Model
The two-zone model, depicted in Figure 88, was developed based on observations
from ozone mass transfer visualization experiments that the near-sparger region (zone 2
[z* > zc*]) has a uniform indigo dye concentration whereas the in the top of the reactor
(zone 1 [z* < zc*]), indigo dye concentration increases monotonically with height. In the
two-zone model, zone 2 is modeled as well mixed (CSTR) and zone 1 is modeled using
the advection-dispersion-reaction model, as in the single-zone model described above.
The term zc* is the “critical” depth separating the two zones.
283
*cz
1* z
Zone 1
Zone 2
1Zone2ZoneFlux2Zone1ZoneFlux
2zone;1zone; ****cIcI zzCzzC
Figure 88: Schematic Diagram, Two-Zone Model
Two-zone models were formulated assuming:
Equal Stanton number in zones 1 and 2
Different Stanton numbers in zones 1 and 2.
The derivation of these models is provided below.
Two Zone Model, Equal Stanton Numbers in Zones 1 and 2
Conservation of gaseous ozone in zone 2 is given as
cOLOGOG zHCakmCUmCU ***0 333
284
HzCUm
aHkCC cO
G
LOO 1***
0 333
Recalling that Stanton number, stripping factor and dimensionless height are
given by
L
LS
U
aHkN
L
G
U
UmS
and
H
zz *
Gaseous ozone concentration in zone 2 becomes
*
*0*
113
3
cS
O
OzSN
CC
(A-18)
Conservation of gaseous ozone in zone 1 is determined by integrating equation A-2 from
z* to zc*
*
*
**3
**3
3
**lnccO
O
z
zS
zC
zCO zSNC
***
*
*0
3
3 ln11
ln zzSNCzS
CcSO
c
O
285
**
3
3 *
*0*
11
zzSN
cS
O
OcSe
zSN
CC
(A-19)
Conservation of aqueous indigo dye in zone 2 is:
ACzHakM
MCQ
dz
dCDACQ OcL
O
IIL
zz
IIL
c
*2, 3
3**
Substitute for *
03OC from equation A-19 and nondimensionalize using 0,*
III CCC and
Hzz * .
*
*0*
2,*
*0,*
0,11
1 3
3** cS
O
cL
L
L
O
IIL
zz
II
IILzSN
CzU
U
aHk
M
MCU
dz
dC
H
CDCCU
c
*
*
*
*0
2,*
*
*
11
13
3** cS
c
I
OL
L
L
O
II
L
zz
ILI
zSN
z
C
C
D
HU
U
aHk
M
MC
D
HUC
D
HU
dz
dC
c
Recall that LLS UaHkN , LG UmUS and DHUP Le and define
0,
*0
0,
*0 3
3
3
3 I
O
O
I
I
O
L
G
O
I
C
CS
M
M
C
C
U
mU
M
M (A-20)
*
**
2,*
*
*
11
1
** cS
ceSIe
zz
IeI
zSN
zPSNCPCP
dz
dC
c
(A-21)
where
data
c
n
niiI
cdataI
I CnnC
C ,
0,
*2,
11(A-22)
286
Conservation of aqueous indigo dye in zone 1 is given by
*
2
2
3
3
OL
O
IIL
I CakM
M
zd
CdU
zd
CdD
Nondimensionalize this expression and substitute for ozone concentration from
equation A-19:
**
3
3
*
*0
2
2
11zzSN
cS
O
L
O
IIL
I cSezSN
Cak
M
M
zd
CdU
zd
CdD
Rearranging this equation and introducing Stanton number, NS, Peclet number, Pe,
stripping factor, S, dimensionless height, z*, and dimensionless indigo dye concentration,
CI* yields the final expression for indigo dye concentration in zone 1.
**
*
*
2
*2
11
1 zzSN
cS
Se
Ie
I cSezSNS
NP
zd
CdP
zd
Cd
(A-23)
Equation A-23 is integrated as follows.
**
*
**
* 11
1 zzSN
cS
SeIe
I cSezSNS
NPCP
zd
dC
zd
d
**
*
**
11
1 zzSN
cS
eIeI cSe
zSNPCP
zd
dC(A-24)
The right hand side (RHS) of equation 20 is evaluated at z* = zc* and equated with the
RHS of equation 17 to determine an expression for the integration constant:
287
eIe PCP *2,
Substitute the result into equation A-24.
**
*
*2,
**
11
1 zzSN
cS
eIeIeI cSe
zSNPCPCP
zd
dC
(A-25)
Equation A-25 is integrated using an integrating factor, yielding
****
*
*2,
*
* 11
1 zzSN
cS
eIezP
IzP cSee e
zSNPCPeCe
zd
d
***
*
*2,
*
11
1 zPzzSN
cSeS
eII
ecS eezSNPSN
PCC
(A-26)
where is an integration constant. The integration constant is determined using the inlet
boundary condition.
*
*
*2,
11
11 cS zSN
cSeS
eI e
zSNPSN
PC
Substitute the integration constant into equation 22 and rearrange for the final expression
for indigo dye concentration in zone 1.
****
**
*
*2,
*
11
1
1
cSecS
ee
zSNzPzzSN
cSeS
e
zPI
zPI
eezSNPSN
P
eCeC
(A-27)
Two Zone Model, Differing Stanton Numbers in Zones 1 and 2
In the two zone model in which Stanton number is allowed to differ in the zones,
288
Stanton number in zones 1 and 2 are designated NS1 and NS2. Proceeding in a manner
similar to that used in the two-zone, single Stanton number model, gaseous ozone
concentration in zone 2 is given by
*2
*0*
113
3
cS
O
OzSN
CC
(A-28)
and concentration of gaseous ozone in zone 1 is given by
**
13
3 *2
*0*
11zzSN
cS
O
OcSe
zSN
CC
Conservation of aqueous indigo dye in zone 2 results in
*
2
*
2*
2,*
*
*
11
1
** cS
ceSIe
zz
IeI
zSN
zPSNCPCP
dz
dC
c
(A-29)
and the conservation of indigo dye in zone 1 is given by
**
1
*2
1*
2
*2
11
1 zzSN
cS
Se
Ie
I cSezSNS
NP
zd
CdP
zd
Cd
(A-30)
Equation A-30 is integrated twice and integration constants are determined using a
Dirichlet boundary condition at the inlet to zone 1 10
**
zIC and, at the discharge of
zone 1 (into zone 2) using the boundary condition
****
*
*
**
*
*
cc zz
IeI
zz
IeI CP
dz
dCCP
dz
dC
289
The resulting expression for indigo dye concentration in zone 1 is
*
1***
1
**
*21
*2,
*
11
1
1
cSecS
ee
zSNzPzzSN
cSeS
e
zPI
zPI
eezSNPSN
P
eCeC
(A-31)
In the limit eS PSN , the expression for indigo dye concentration becomes
*2
**
2,*
111
**
**
cS
zzPezP
IzP
IzSN
ezPeCeC
ce
ee
(A-32)
290
APPENDIX D: R SCRIPT FOR BEST FIT PARAMETERS ESTIMATION
cIndigo <- function(S1Hat, PeHat, S2Hat){exp(PeHat*Exp_Data2$zstar) +PeHat*psi*(exp(-S1Hat*(zc-Exp_Data2$zstar))-exp(-
S1Hat*zc+PeHat*Exp_Data2$zstar))/(S1Hat-PeHat)/(1+S2Hat*(1-zc)) +(CI2+psi)*(1-exp(PeHat*Exp_Data2$zstar))}
CIndigo <- function(p) {-sum((Exp_Data$MEAN - cIndigo(p[1],p[2]))^2)}
Exp_Data <- read.table("C:/Documents and Settings/Carolyn/MyDocuments/TBFiles/O3/IndigoPics/Finals/05_25_06/MEANS2_by16_Gurian.DAT",header=TRUE)
par(fig=c(0.025,0.975,0.025,0.975),mai=c(0.85,0.85,0.05,0.05))plot(Exp_Data$zstar,Exp_Data$MEAN,type="l",xlab=expression(z^a),ylab=expression(C[O[3]]^2),ylim=c(0,1))psi <- 1.1926
PeGuess <- 4S1Guess <- 1S2Guess <- 0
#### Plot model line using initial gueses##
ndata <- length(Exp_Data$zstar)nmin <- round(3*ndata/5)nmax <- ndata-1
nc <- nminzc <- Exp_Data$zstar[nc]
CI2 <- sum(Exp_Data$MEAN[nc:ndata])/(ndata - nc+1)SSE2 <- sum((Exp_Data$MEAN[nc:ndata]-CI2)^2)SSE2
MEAND <- Exp_Data$MEAN[1:nc]ZD <- Exp_Data$zstar[1:nc]Exp_Data2 <- data.frame(zstar=ZD, MEAN=MEAND)CI2min <- min(Exp_Data$MEAN)DCI2 <- MEAND[nc]-CI2minDCI2S2GuessX <- DCI2/(1-zc)/(psi-DCI2)S2Guess <- max(0,S2GuessX)S2GuessC <- cIndigo(S1Guess,PeGuess, S2Guess)lines(Exp_Data2$zstar,C,col="red")
Errs <- seq(length=ndata, from=-1e+6,by=0.000001)
291
PeEstS <- seq(length=ndata, from=-1e+6,by=0.000001)S1EstS <- seq(length=ndata, from=-1e+6,by=0.000001)S2EstS <- seq(length=ndata, from=-1e+6,by=0.000001)
for (i in nmax:nmin) {nc <- izc <- Exp_Data$zstar[nc]ndata <- length(Exp_Data$zstar)
CI2 <- sum(Exp_Data$MEAN[nc:ndata])/(ndata - nc+1)SSE2 <- sum((Exp_Data$MEAN[nc:ndata]-CI2)^2)SSE2
MEAND <- Exp_Data$MEAN[1:nc]ZD <- Exp_Data$zstar[1:nc]Exp_Data2 <- data.frame(zstar=ZD, MEAN=MEAND)CI2min <- min(Exp_Data$MEAN)DCI2 <- MEAND[nc]-CI2minDCI2
genga <- nls.control(maxiter=10000,tol=1e-6,minFactor=0.000488281/128)outIndigo <- nls(MEAND ~ cIndigo(S1Est,PeEst, S2Est),Exp_Data2,start=
list(S1Est=S1Guess,PeEst=PeGuess,S2Est=S2Guess),genga,lower=c(0,0,0),algorithm="port")
AA <- coef(outIndigo)BB <- residuals(outIndigo)CC <- fitted.values(outIndigo)SSE1 <- sqrt(sum(BB^2))SSE1SSE2SSE <- SSE1 + SSE2SSE
S1Est <- AA[1]S1Guess <- S1EstPeEst <- AA[2]PeGuess <- PeEstS2Est <- AA[3]S2Guess <- S2EstiPeGuessS1GuessS2Guess
## CI <- cIndigo(S1Est,PeEst,S2Est)
lines(Exp_Data2$zstar,CC,col="blue")
zz <- Exp_Data$zstar[1:nc]CO31 <- exp(-S1Est*(zc-zz))/(1+S2Est*(1-zc))lines(zz,CO31,col="orange")
292
z2line <- c(zc,1)CI2line <- c(CI2,CI2)CO32 <- 1/(1+S2Est*(1-zc))CO3Line <- c(CO32,CO32)lines(z2line,CI2line,col="blue")lines(z2line,CO3Line,col="orange")
Errs[i] <- SSES1EstS[i] <- S1EstS2EstS[i] <- S2EstPeEstS[i] <- PeEst}
ii <- seq(length=(nmax-nmin+1),from=nmin,by=1)imin <- which.min(abs(Errs))iminErrmin <- Errs[imin]ErrminErrmin <- min(abs(Errs))ErrminErrmax <- max(Errs)Errmaxplot(ii,Errs[nmin:nmax],xlab=expression(n[c]),ylab="SSE",ylim=c(Errmin,Errmax))points(imin,Errmin,col="red",cex=1.3,pch=19)
## Make a pretty plot showing fitted curves (indigo and ozone) and data
windows()par(fig=c(0.025,0.975,0.025,0.975),mai=c(0.85,0.85,0.05,0.05),family="serif",xaxs="r")gc <- grey(0:8 / 8)plot(Exp_Data$zstar,Exp_Data$MEAN,type="p",xlab="Normalized Depth(z*)",
ylab="Normalized Concentration",ylim=c(0,1),
xlim=c(0.2,1.0),col=gc[2],family="serif",cex.axis=1.25,cex.lab=1.25)
nc <- iminnczc <- Exp_Data$zstar[nc]zc
S1Guess <- S1EstS[imin]S1GuessS2Guess <- S2EstS[imin]S2GuessPeGuess <- PeEstS[imin]PeGuess
CI2 <- sum(Exp_Data$MEAN[nc:ndata])/(ndata - nc + 1)SSE2 <- sum((Exp_Data$MEAN[nc:ndata]-CI2)^2)
293
SSE2
MEAND <- Exp_Data$MEAN[1:nc]ZD <- Exp_Data$zstar[1:nc]Exp_Data2 <- data.frame(zstar=ZD, MEAN=MEAND)genga <- nls.control(maxiter=100000,tol=1e-5)outIndigo <- nls(MEAND ~ cIndigo(S1Est,PeEst,S2Est),Exp_Data2,
start=list(S1Est=S1Guess,PeEst=PeGuess,S2Est=S2Guess),genga,lower=c(0,0,0),algorithm="port")
summary(outIndigo)iminExp_Data$zstar[imin]
AA <- coef(outIndigo)BB <- residuals(outIndigo)CC <- fitted.values(outIndigo)
S1Est <- AA[1]PeEst <- AA[2]S2Est <- AA[3]
SSE1 <- sqrt(sum(BB^2))SSE1SSE2SSE <- SSE1 + SSE2SSE
CI <- cIndigo(S1Est,PeEst,S2Est)
lines(Exp_Data2$zstar,CC,col="black",lwd=2)
zz <- Exp_Data$zstar[1:nc]CO31 <- exp(-S1Est*(zc-zz))/(1+S2Est*(1-zc))
z2line <- c(zc,1)CI2line <- c(CI2,CI2)CO32 <- 1/(1+S2Est*(1-zc))CO3Line <- c(CO32,CO32)lines(z2line,CI2line,col="black",lwd=2)legend(0.5,0.3,legend=c(expression(C[I]^"\*"*"\ "*"(Experimentaldata)"),expression(C[I]^"\*"*"\ "*"(Fitted model)")),col=c(gc[2],gc[0]),lty=c(0,1),lwd=c(1,2),bty="n",pch=c(1,26),y.intersp=1.3,cex=1.25,pt.cex=0.75)
#### Perform runs test on the residuals. Convert residuals to binaryarray and## factor, then perform the runs test##
ResBi <- sign(BB)
294
ErrB <- seq(length=nc, from=-1e+6,by=0.000001)for (i in 1:nc) {ErrB[i] <- max(0,ResBi[i]) }ErrBF <- factor(ErrB)runs.test(ErrBF,alternative="two.sided")
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Vita
Timothy Allen Bartrand was born in Muskegon, Michigan, USA, on Octboer 19th,
1961 to Loren L. Bartrand and Donna Hickey Bartrand. Mr. Bartrand attended Rogers
High School, Wyoming, MI, graduating the class valedictorian. Upon graduation from
high school Mr. Bartrand undertook undergraduate studies at the University of Notre
Dame, Notre Dame, IN, earning a bachelor’s degree in aerospace engineering in May,
1983. In June, 1983, Mr. Bartrand began service as a Peace Corps volunteer, teaching
mathematics and physics at the Union Comprehensive Secondary School in Bachuo
Akagbe, Manyu Division, Southwest Province, Cameroon. He is married to Carolyn
Davis and they have one daughter, Olivia Davis Bartrand.
Mr. Bartrand has earned two masters degrees: a master of science in mechanical
engineering from the University of Tennessee (awarded 12/87, thesis title “A Study of
Low-Frequency Combustion Instability in Rocket Engine Preburners using a
Heterogeneous Stirred Tank Reactor Model”) and a master of science in civil engineering
from Ohio University (awarded 12/97, thesis title “Experimental Investigation of a
Vacuum Apparatus for Zebra Mussel Control in Closed Conduits”).
Mr. Bartrand’s professional experience includes eight years as a research engineer
working as a NASA Lewis Research Center on-site contractor, three years experience
developing water and sanitation facilities in relief settings and one year as an
environmental regulator for the Ohio EPA.
